STATISTICS FOR MANAGEMENT CONTENTS 1. Introduction to Statistics 2. Probability 3. Probability Distribution 4. Sampling & Sampling Distribution 5. Estimation 6. Testing of Hypothesis 7. Chi-Square & ANOVA 8. Simple Correlation & Regression 9. Business Forecasting & Time Series 10. Index Numbers UNIT 1 1. Which of the following statements about statistics is not correct? a. Statistics is sometimes misused by statistians b. Statistics has hardly any limitations c. Statistics is Indispensable in Management of business enterprises d. Statistics is of two types – descriptive is inferential 2. Which of the following is a primary data a. Census of population data b. Whole sale price Index Numbers c. Statistics contained in an official publication d. Data collected through your own field survey 3. Collection of secondary data is a. Cheaper b. Faster c. More accurate d. a & b e. a, b & c 4. Which of the following is the most accurate method of classifying data a. Qualitative method b. Quantitative method c. Method depending on the Nature of Information d. a & b 5. Which Tabulating the grouped data: a. Each group must have frequencies
Transcript
STATISTICS FOR MANAGEMENT
CONTENTS1. Introduction to Statistics2. Probability3. Probability Distribution4. Sampling & Sampling Distribution5. Estimation6. Testing of Hypothesis7. Chi-Square & ANOVA8. Simple Correlation & Regression9. Business Forecasting & Time Series10. Index Numbers
UNIT 1
1. Which of the following statements about statistics is not correct?a. Statistics is sometimes misused by statistians b. Statistics has hardly any limitationsc. Statistics is Indispensable in Management of business enterprisesd. Statistics is of two types – descriptive is inferential
2. Which of the following is a primary data a. Census of population datab. Whole sale price Index Numbersc. Statistics contained in an official publication d. Data collected through your own field survey
3. Collection of secondary data is a. Cheaperb. Fasterc. More accurated. a & be. a, b & c
4. Which of the following is the most accurate method of classifying dataa. Qualitative methodb. Quantitative methodc. Method depending on the Nature of Informationd. a & b
5. Which Tabulating the grouped data:a. Each group must have frequenciesb. Frequency can be Negativec. It is necessary to have frequenciesd. None of the above
6. The first step in the following of a frequency Table is:a. Choosing a suitable size or width of class intervalb. Establishing the boundaries of each class Intervalc. Deciding an appropriate Number of class groupingd. Classifying the data into appropriate classes
7. In a relative frequency distribution, frequencies are in
a. Whole numbersb. Percentagesc. Fractionsd. Both b & c
8. The Numbers of classes in a frequency distribution depends ona. Range of observationb. Size of populationc. Number of data pointsd. a & ce. a, b and c
9. The upper limit of class Intervals is required when we consider the formation ofa. Relative frequencyb. ‘More than’ cumulative frequencyc. ‘Less then’ Cumulative Frequencyd. None of the above
10.Which of the following is not an example of compressed dataa. A frequency curveb. Frequency distributionc. Data arrayd. Histogram
11. In a frequency distribution, classes are all inclusive becausea. The given data must fit into one class or anotherb. None of the data points falls into more than one classc. There are always more classes than data pointsd. All of these
12.While preparing a frequency Table, which of the following number of classes is generally used
a. Less than fiveb. Between 5 and 10c. Between 10 and 20d. None of these
13.Double counting is a result of _______ or ________a. Primary, secondaryb. Qualitative, Quantitativec. Probability, Non-probabilityd. None of these
14.When calculating the average rate of debt expansion for a company the correct mean to use is the
a. Arithmetic meanb. Weighted meanc. Geometric meand. Either a or c
15.The Mode has all of the following disadvantages excepta. A data set may have no modal valueb. Every value in a data set may be modec. A multimodal data set is difficult to analyzed. The mode is unduly affected by extreme values
16.What is the major assumptions we make while calculating mean from grouped data?a. All values one discreteb. Every value in the class is equal to midpointc. No value occurs more than onced. Each class contains exactly the same number of values
17.Which of the statements is NOT Correct?a. Some data sets do not have Meansb. Calculation of Mean is affected by Extreme valuesc. A weighted mean should be taken when it is necessary to take the Importance of
each value into accountd. All these statements are correct
18.Which of the following is first step in calculating the median of a data set?a. Average the middle two values of data setb. Array the datac. Determine the relative weight of data values in terms of importanced. None of these
19.Which of the following is not an advantage of using a median?a. Extreme values affect the median less strongly than they do the meanb. A median can be calculated for qualitative descriptionsc. Median is easy to understandd. All the above are advantages
20.Why is it usually better to calculate mode from grouped, rather than ungrouped data?a. The ungrouped data tend to be bimodalb. The mode for the grouped data will be samec. Extreme values have less affect on grouped datad. The chance of an unrepresentative being chosen as the mode is reduced
21. In which of these cases would the mode be most useful as an indicator of central tendency?
a. Every value in a data set occurs exactly onceb. All but three values in a data set occur once; three values occur 100 times eachc. All values in data set occur 100 times eachd. Every observation in a data set has the same value
22.Which of the following is an example for a parameters?a. ¯xb. ηc. µd. all of thesee. b and c but not a
23.Which of the following is NOT a measure of central tendency?a. Geometric meanb. Medianc. Moded. Arithmetic meane. Mean deviation
24.When the distribution is symmetrical and has one mode, the highest point on curve is called?
a. Rangeb. Modec. Mediand. Meane. All of thesef. b, c & d
25.When referring to a curve that tails off to the left end, you would call ita. Symmetricalb. Skewed rightc. Positively skewedd. All of thesee. None of these
26.Disadvantage of using the Range as a measure of dispersion include all of the following except
a. It is heavily influenced by extreme valuesb. It can change drastically from one sample to the nextc. It is difficult to calculated. It is determined only two points in the data set
27.Why it is necessary to square the difference from the mean when computing the population variance
a. So that extreme values will not affect the calculationb. Because it is possible that N could be very smallc. Some of the differences will be +ve & some one –ved. None of these
28.Assume that population has µ=100 and σ = 10, If a particular observation has a standard score of 1, It can be concluded that
a. Its value is 110b. It lies L/n 90 and 110c. Its value is greater than 110d. Nothing can be determined without knowing N
29.Assume that a population has µ = 100 and σ = 10, and N=1000. According to chebyshev’s theorem, which of the following situations is NOT possible?
a. 150 values are greater than 130b. 930 values lie between 100 & 108c. 22 values lie between 120 & 125d. 70 values are less than 90e. All these situations are possible
30.Which of the following is an example of relative measure of dispersiona. Standard deviationb. Variancec. Co-efficient of varianced. All of thesee. a and b
31.Which of the following is True?a. The variance can be calculated for grouped or ungrouped datab. The S.D can be calculated for grouped or ungrouped datac. Variance can be calculated for only ungrouped datad. a and b
32. If one was to divide the stand and deviation of a population by the mean of the same population and multiply this value by 100, one would have calculated the
a. Population stand and scoreb. Population variancec. Population standard deviationd. Population coefficient of variatione. None of these
33.How does the computation of a sample variance differ from computation of a population variance
a. µ is replaced by x b. N is replaced by (n – 1)c. N is replaced by nd. a and ce. a and b
34.The square of the variance of a distribution is the a. Standard deviationb. Meanc. Ranged. Absolute deviatione. a and bf. None
35.Chebyshev’s theorem says that 99% of the values will be within ± 3 S. D from the mean for-
a. Bell shaped distributionsb. Positively skewed distributionsc. Left-tailed distributiond. All distributionse. No distributions
36.The mean of 10, 20, 30, 40, 50 will be a. 50b. 49c. 48d. 51
37. In the formula x = A + Σ fd / N, The ‘d’ can be calculated bya. X – Ab. x – xc. N – Ad. None
38. In a class of 60 students 10 have failed with an average marks of 15. If the total marks of all the students is 1800. The average marks of those who have passed will be
a. 29b. 34c. 33d. 42
39.An average monthly production of a certain factory for the first eight months is 3546 units and for remaining four months is 3100 units. The average monthly production for the year will be _____
a. 3397.33 unitsb. 3497.33 unitsc. 3597.33 unitsd. 3697.33 units
40.The mean weight of 150 workers in a factory is 45 Kgs. If the mean weight of men is 64 Kgs. And that of women is 48 Kgs. The Number of men and women workers in factory are
a. 75 and 75b. 50 and 100c. 60 and 90d. 100 and 50
41.The mean wages paid to 1000 workers in a factory was found to be Rs. 180.40 Later on it is discovered that the wages of two employees were taken wrongly as 297 and 165 instead of 197 and 185. therefore correct mean wages are
a. Rs. 178.85b. Rs. 180c. Rs. 181.49d. Rs. 180.32
42. If x1 = 275, N1 = 100, x2 = 225 and N2 = 80 The value of x isa. 264.77b. 252.77c. 249d. 248.77
43.Mean marks of Nine students is 39, Eight students marks are available as 25, 36, 48, 52, 39, 41, 27 and 38. The missing marks of Ninth student is ______
a. 51b. 49c. 45d. 48
44.Mean of 20 values is 45. If one of the values is to be taken as 64 instead of 46, the correct mean is
a. 45.2b. 45.4c. 45.9d. 45.7
45. If the average wages paid to 25 workers is Rs. 79.60. The missing frequencies one _____ & _______Wages: 50 60 70 80 90 100 110Workers 1 3 ? ? 6 2 1
From the above data, Answer the following questions:
63.The value of mode will be _______a. 120b. 140c. 100d. 180
64.The value of M. D. will bea. 28b. 28.69c. 27d. 28.42
65.The value of coefficient of M. D will bea. 0.239b. 0.230c. 0.24d. 0.25
66. If the value of variance is 100 The S. D will bea. 10b. 100c. 50d. 25
67. If x = 56 and variance = 144. The value of C. V is _______a. 17.5b. 19c. 21.42d. 20
68.Σ x = 160, n= 20, variance = 16. Find the value of C. Va. 4 b. 6c. 8d. 10
69. In a distribution, variance=121, C. v = 23.16%. the value of mean is a. 49b. 47.49c. 46d. 48.5
Questions 70 - 71Arithmetic mean of runs scored by 3 batsmen Dilip, Kumar and Santosh in a series of 10 Innings are 50, 48 and 12 respectively. The stand and deviation of their runs are respectively 15, 12 and 2 respectively. Answer the following questions:
70.Who is the most consistent?a. Dilip
b. Kumarc. Santoshd. None
71.Who is the better scores?a. Dilipb. Kumarc. Santoshd. None
72.C. V of the series is 58% and σ = 21.2 The value of mean is a. 38b. 36.55c. 37d. 34.92
From the above data, Answer the following questions:
73.The total n. of persons employed in these companies are _____a. 5150b. 5200c. 5400d. 5250
74.The value of mean is _________a. 128b. 128.25c. 128.50d. 128.75
75.The value of S. D is __________a. 100b. 100.10c. 100.24d. 101
76.The value of CV is ________a. 74%b. 72%c. 77.85%d. 76%
Questions 77 - 82An analysis of the monthly wages paid to the workers in two firms A and B belonging to the same industry gives the following results:
A BNo. of Workers 500 600Average monthly wages Rs. 186 Rs. 175Variance Rs. 81 Rs. 100
77.Which firm has a longer wage bill a. Ab. B
78.The S. D for firm A will bea. 9b. 10c. 12d. 14
79.The S. D. for the firm B will be _________a. 12b. 14c. 10d. 16
80.Which firm has greater variability in individual wages?a. Ab. B
81.The C. V of the firm A will bea. 5%b. 4.84%c. 6.20%d. 8.90%
82.The C .V of the firm B will bea. 5.71%b. 6.20%c. 5.84%d. 6.29%
83. In a distribution the following results were given, maximum value = 60 and co-efficient of range is 0.6. the value of range is ________
a. 45b. 40c. 50d. 60
84.The upper and lower quartile Income of a group of workers are Rs. 8 and Rs. 3 per day respectively. The Q. D. will be
a. 2.9b. 2.5c. 3.2d. 4.2
85. If Q. D. = 40 Find S. D. a. 60b. 70c. 75d. 80
86. If M. D = 16, find S. Da. 20
b. 25c. 40d. 60
87.G. M of 2, 4 and 8 will be ___________a. 8b. 4c. 6d. 2
88.H.M of 4, 8, 16 will be _______a. 4.9b. 5c. 6.86d. 8.96
89.Cities A, B and C are equidistant from each other. A motorist Kavels from A to B at 30 km/hr from B to C at 40 km/hr and from C to a at 50 km/hr. Determine the average speed for the entire trip.
a. 38.3 km/hrb. 40 km/hrc. 42 km/hrd. 46 km/hr
90.The G. M for 4, 16 and 8 is a. 6b. 10c. 12d. 8
91.The standard deviation of a population dividend by the mean and multiplied by 100 results into ___________
a. Standard scoreb. Variancec. Co-efficient of varianced. None of these
UNIT – 2
92. If one event is unaffected by the outcome of another event, the two events are said to be ______
a. Dependentb. Independentc. Mutually exclusived. All the abovee. Both b & c
93. If (P[A or B]) = P (A), Then a. A and B are mutually exclusiveb. The Venn diagram areas for A and B overlapc. P(A) + P(B) is joint probability of A and Bd. No of the above
94.The simple probability of an occurance of an event is called thea. Bayesian probability
b. Joint probabilityc. Marginal probabilityd. Conditional probability
95.Why are the events of a coin toss mutually exclusive?a. The outcome of any toss is not affected by the outcomes of those preceeding itb. Both a head and a tail cannot turn up on any one tossc. The probability of getting a Head and tail are samed. a and b
96. If a Venn diagram were drawn for events A and B, which are mutually exclusive which of the following would be True of A & B.
a. Their parts of the rectangle will overlapb. Their parts of rectangle will be equal in areac. Their parts of rectangle will not overlapd. b and c
97.What is the probability that a value chosen at random from a particular population Is larger than the median of the population
a. 0.25b. 0.5c. 1d. 0.67
98.Assume that a single fair dice is rolled once. Which of the following is True?a. The probability of rolling a number higher than 1 is 1 – p (1 is rolled)b. The probability of rolling 3 is 1 – p (1, 2, 4, 5 or 6 is rolled)c. The probability of rolling 5 or 6 is higher than the probability of rolling 3 or 4d. All of thesee. A and b
99. If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B). How does the calculation of P(A or B) change if A and B are not mutually exclusive?
a. P(AB) must be subtracted from P(A) + P(B)b. P(AB) must be added to P(A)+ P(B)c. [PA) + P(B)] must be multiplied by P(A or B)d. [P(A) + P(B)] must be divided by P(AB)e. None of these
100. Assume that a die is rolled twice in succession and that you are asked to draw the probability tree showing all possible outcomes of the Two rolls. How many branches will your tree have?
a. 6b. 12c. 36d. 42e. 48
Ten numbered balls are laced in an urn. Nos., 1 – 4 are red and nos. 5 – 10 are blue[NOTE: Questions 101, 102, 103 refer to this situation]
101. What is the probability that a ball drawn at random from the urn in blue?a. 0.1b. 0.4c. 0.6
d. 1.0e. Cannot be determined
102. The probability of drawing the ball Numbered 3, of course is 0.1. A ball is drawn, and it is red. Which of the following is True?
a. P[red] = 0.1b. P[red] < 0.1c. P[red] < 0.1d. P[red] = 0.25e. c and d
103. In question 102, the probability of drawing the 3 ball was reconsidered after it was found that the ball drawn was Red. The New probabilities we considered are called
a. Exhaustiveb. A prioric. Marginald. Subjectivee. None of these
104. Symbolically, a marginal probability isa. P(AB)b. P(BA)c. P(B/A)d. P(ABC)e. None of these
105. If we sum all the probabilities of the conditional events in which the event A occurs while under statistical dependents. The result is ___________
a. Marginal probability of Ab. Joint probability of Ac. Conditional probability of Ad. None of these
106. One of the possible outcomes of doing something is a __________. The activity that produced this outcome is a ____________
a. Event, Sampleb. Event, Experimentc. Sample, Experimentd. Random, Experiment
107. The set of all possible outcomes of an activity is the _________a. Random Experimentsb. Trailc. Resultsd. Sample space
108. A pictorial representation of probability concepts, using symbols to represent outcomes, is a _________
a. Histogramb. Venn diagramc. Bar graphd. O-give graph
109. Events that cannot happen together are called _____________a. Unfavorable events
b. Favorable eventsc. Mutually exhaustived. Mutually exclusive
110. The probability of one event occurring given that another event has occurred, is called _____ probability
a. Conditionalb. Marginalc. Subjectived. Classical
111. In terms of its assumptions, the least restrictive approach to the study of probability is the ________
a. Classical approachb. Conditional approachc. Baysian approachd. Subjective approach
112. ________ theorem is often used in Management Decision Making processa. Bayes’b. Charle’sc. Axiomaticd. Multiplication
113. A list is _____ if it includes all the possible outcomes that can result from an experiment
a. Mutually exhaustiveb. Mutually exclusivec. Collectively exhaustived. Subjective
114. P(5) = ___________a. 1b. 0.5c. 0.25d. 0.75
115. Assuming that a box contains in all ten balls of which six are green and four are red, what is the probability of drawing a Red ball?
a. 0.1b. 0.5c. 1.0d. 0.4
116. What is the probability of getting an Even no. when a die is rolled?a. 1/3b. ½c. 1/6d. 1
117. What is the probability of getting more than 2 when a die is rolled?a. 1/3b. ½c. 2/3d. 1
118. What is the probability of getting a Total of 5 when a pair of die & rolled off simultaneously?
a. 1/36b. 1/12c. 4/9d. 1/9
119. If P(AB) = 0, Then two events A and B are said to bea. Dependentb. Independentc. Equally likelyd. None of these
120. Baye’s Theorem is useful ina. Computing conditional probabilityb. Computing sequential probabilityc. Revising prior probabilityd. None of these
121. What is the probability of drawing an ace from a bunch of playing cards?a. 1/10b. 1/13c. 1/52d. None of those
122. The probability of getting a head, while tossing a coin three times is a. 1b. 0.75c. 0.25d. 0.125
123. What is the probability of getting three heads or three tails on three successive tosses?
a. 0.25b. 0.125c. 0.175d. None of these
124. In a single throw with two dice, what is the probability of getting a total of 9?a. 1/24b. 1/16c. 1/12d. 1/9
125. In a throw of dice, find the probability of obtaining a number greater than 2a. 1/3b. 2/3c. 4/3d. 1
126. Find the value of 4!a. 29b. 19c. 36
d. 24
127. Find the number of permutations of the word ACCOUNTANTa. 226800b. 275900c. 62500d. 43200
128. How many Five Letter words an be formed from the word LOGARITHMSa. 30240b. 30250c. 30260d. 30270
129. A bag contains 4 white and 6 black balls Two balls are drawn out together. What is the probability that both are black?
a. 1/3b. 2/3c. ¼d. 1
130. From 10,000 Lottery tickets Numerical from 1 to 10,000, one ticket is drawn at Random What is the probability that number marked on drawn ticket is divisible by 20?
a. 0.06b. 0.05c. 0.08d. 0.92
131. Two letters are drawn at Random from the word HOME. Find the probability that atleast one is a Vowel.
a. 5/6b. 1c. 4/6d. 2/6
132. A bag contains 5 red, 3 white and 6 green balls. Three balls are randomly drawn. What is the probability that a red, a white and a green ball is drawn?
a. 24/91b. 16/91c. 29/91d. 82/91
133. A bag contains 4 white and 6 black balls. Two balls are drawn out together. What is the probability that both are black?
a. 1/4b. 1/3c. 2/6d. 1/3
134. Four cards are drawn from a pack. Find the probability that there is one card from each suit
a. 0.10b. 0.25c. 0.64d. 0.32
135. Given P(A) = 0.5 P(A ∩ B) = 0.2 Find the value of P (A U B) = ?a. 3/5b. 2/5c. 6/9d. 4/8
UNIT 3
Probability Distribution
136. For a given Binomial distribution, with n fixed if P < 0.5, Thena. Poisson distribution will provide a good approximation b. Poisson distribution will provide a bad approximationc. Binomial distribution will be skewed leftd. Binomial distribution will be skewed Righte. Binomial distribution will be symmetric
137. Suppose we have poisson distribution with λ = 2 Then probability of having exactly 10 occurences is
138. Which of the following is a characteristic of the probability distribution for any random variable?
a. A probability is distributed for any randomb. The sum of all probabilities is 1c. No given probability occurs more than once d. All of thesee. a and b
139. Which of the following could be Never described by Binomial distributiona. The No. of defective widgetsb. The amount of water used dailyc. The No. of people in your class who answer this question correctlyd. All the above
140. If P = 0.4 for a particular B. d, The calculation 7! (0.4)3 (0.6)4
3! X 4!
Gives the probability of gettinga. Exactly three successes in seven trailsb. Exactly four successes in seven trailsc. Three or more successes in seven trailsd. Four or more successes in seven trailse. None of the above
141. For a binomial distribution with p=0.2 a. A distribution for n = 2000 would more closely approximate the Normal
distribution than one for n = 50b. No matter what the value of n, The distribution is skewed to the right.c. The graph of this distribution with p=0.2 and n=100 would be the exact reverse of
the graph for the binomial distribution with n=100 & p=0.8
d. All of thesee. a and b
142. Which of the following is a necessary condition for use of a poisson distribution a. Probability of one arrival per second is consistentb. The No. of arrivals in any 1 second Interval is independent of arrivals in another
intervalsc. The probability of two or more arrivals in the same second is zerod. All of thesee. None of these
143. In which case would the poisson distribution be a good approximation of binomiala. n=40, p=0.32b. n=40, q=0.79c. n=200, q=0.98d. n=10, q=0.98e. n=10, p=0.03f. a and cg. all of these
144. A binomial distribution may be approximated by a poisson distribution If a. n is large & p is largeb. n is small & p is largec. n is small & p is smalld. None of thesee. A and b
145. The standard deviation of a binomial distribution depends ona. Probability of successb. Probability of failurec. Number of trialsd. a and be. b and cf. a, b & c
146. The weighted average of the outcomes of an experiment is referred to as the _________
a. Random valueb. Probability valuec. Expected valued. None
147. The distribution that deals only in successes and failures is referred to as the _______ distribution
a. Binomial distributionb. Poisson distributionc. Normal distributiond. Exponential distribution
148. When approximating a binomial distribution by a Normal distribution, a __________ correction factor should be used
a. Discreteb. Continuityc. Randomd. Probability
149. The mean (µ) of Binomial distribution is calculated by formulaa. nqb. npc. npqd. √npq
150. The standard deviation of Binomial distribution (σ) is given bya. nqb. npc. npqd. √npq
151. For a poisson distribution, the symbol that represents the mean number of occurances per interval of time is _________
a. µb. λc. σd. α
152. A list of probabilities of outcomes that could result If an experiment were performed is called a _________
a. Sample spaceb. Theoretical distributionc. Random experimentd. Probability distributione. Both b and d
153. The two parameters necessary to describe a Normal distribution are ______ & ______
a. Mean & medianb. Mean & modec. Median & Standard deviationd. Mean & Standard deviation
154. A _______ variable is a variable that assumes different values according to results of an experiment
a. Probabilityb. Discretec. Randomd. Normal
155. The formula to calculate standard normal variable (2) is given bya. X - µ / σb. X - σ / µc. µ - σ / Xd. None
156. If the expected profit of a business firm for January 2005 is Rs. 10 lakh Then the profit for February will be
a. Rs. 10 Lakhb. Less than Rs. 10 lakhc. More than Rs. 10 lakhd. None
157. The standard deviation of binomial distribution depends on a. Probability of successb. Probability of failurec. Number of trailsd. All the above
158. In the context of Binomial distribution. If on an average 8 ships out of 10 arrive safely at ports and 150 ships have returned safely. The mean is
a. 80b. 100c. 120d. 150
159. A Normal distribution curve isa. Symmetrical b. Has a single peakc. Mean located at centred. Mean, median & mode are samee. All the above
160. If a normal distribution has µ = 25 and the mode will be _______a. 15b. 50c. 25d. None
161. Suppose the probability of dialing a wrong number is 0.05. then the probability of dialing exactly 3 wrong numbers in 100 trials is
a. 0.18b. 0.23c. 0.14d. 0.27
162. For a Binomial distribution, n=10, p=0.4 Find Standard deviationa. 1.48b. 1.96c. 2d. 1.46
163. For a binomial distribution, n=12 and p=0.45 find P(r=8)a. 0.0762b. 0.846c. 0.924d. 0.8456
164. Find P(r > 4)a. 0.78b. 0.6955c. 0.34d. 0.82
165. Find P[ r ≤ 10]a. 1b. 0.9989c. 0.428
d. 0.634
166. Find mean and standard deviation of following Binomial distribution n=16, p=0.40a. 6.4, 1.9b. 6.8, 1.42c. 6.9, 1.9d. 6.4, 2.4
167. The probability of dialing a wrong number is 0.05, What is the probability of dialing exactly 3 wrong numbers in 100 dials?
a. 0.82b. 0.62c. 0.14d. 0.43
168. X is distributed normally with µ = 5 and σ = 2. find the value of P(Z = 8)a. 1.5b. 2.0c. 4.3d. 4.9
169. In a Binomial distribution, x = 2, n = 4 and p = 1/3. then P(x = 2) = ?a. 0.296b. 0.456c. 0.896d. 0.143
170. The Number of accidents in a year attributed in a city follows poisson distribution with mean 3 out of 1000 Taxi drivers, find approximate No. of drivers with No accident
UNIT 4
Sampling & Sampling Distribution
171. Which of the following is a method of selecting samples from populationa. Judgement samplingb. Random samplingc. Probability samplingd. All of thesee. a & b
172. Choose the pair of symbols that best completes this sentence _____ is a parameters, whereas ________ is a statistic
a. N, µb. Σ, Sc. N, nd. All of thesee. B & c
173. In random sampling. We can describe mathematically how objective our estimates are, why is this?
a. We always know the chance that any population element is included in the sample
b. Every sample always has an equal chance of being selected
c. All the samples are of exactly same sized. None of thesee. a and b
174. Suppose you are performing stratified sampling on a particular population ?& have divided it into strata of different sizes. How can you now make your sample selection?
a. Select at random an equal number of elements from each stratum b. Draw equal No. of elements from each stratum and weigh the resultsc. Draw numbers of elements from each stratum proportional to their weightsd. a and be. b and c
175. In which of the following situations would σx = σ / √n be the correct formula to use for computing σx ?
a. Sampling is from Infinite populationb. Sampling is from finite population with replacementc. Sampling is from infinite population without replacementd. a and be. b and c
176. The dispersion among sample means is less than the dispersion among the sampled items themselves because
a. Each sample is smaller than populationb. Very large value are averaged downc. Sampled items are all drawn from the same populationd. None of thesee. b and c
177. Suppose that a population with N = 144 and µ = 24. What is the mean of the sampling distribution of mean for samples of size 25?
a. 24b. 2c. 4.8d. Cannot be determined
178. The control limit theorem assures us that the sampling distribution of mean a. is always Normalb. is always normal for large sample sizesc. approaches normality as sample size increasesd. appears normal only when N > 100
179. The finite population multiplier does not have to be used when the sampling fraction is
a. Greater than 0.05b. Greater than 0.50c. Less than 0.50d. Greater than 0.90e. None of these
180. The standard error of the mean for a sample size of two or more isa. Always greater than Standard deviationb. Generally greater than Standard deviationc. Usually less than Standard deviationd. None of these
181. A border patrol check point that stops every passenger van is usinga. Simple Random samplingb. Systematic samplingc. Stratified samplingd. Complete enumeration
182. In a Normally distribution population. The sampling distribution of the meana. Is normally distributedb. Has a mean equal to population mean c. Has a Standard deviation equal to population Standard deviation divided by
square root of sample size d. All the abovee. Both a and b
183. A portion of the elements in a population chosen for direct examination or measurement is a ____________
a. Eventb. Samplec. Errord. Enumeration
184. The proportion of the population contained in a sample is the _________a. Sampling fractionb. Event fractionc. Measurement fractiond. None
185. ___________ is the process by which inferences about a population are made from information about a sample
a. Mathematical inferenceb. Statistical inferencec. Probability inferenced. None
186. The __________ is the distribution obtained by finding the sampling distribution of all samples of given size of population
a. Theoretical sampling distributionb. Probability distributionc. Poisson distributiond. Estimation
187. _______ sampling should be used when each group considered has small variation within itself but there is wide variation between different groups
a. Stratifiedb. Systematicc. Precisedd. None
188. A method of random sampling in which elements are selected from the population at uniform intervals is called __________ sampling
a. Stratifiedb. Systematicc. Precisedd. None
189. __________ is the degree of accuracy with which the sample mean can estimate the population mean
a. Relativeb. Measurec. Precisiond. None
190. A sampling distribution of the proportion is a probability distribution of the _________
a. Random proportionsb. Sample proportionsc. Irregular proportionsd. None
191. Which of the following is NOT a probability sample design?a. Stratified sampleb. Multi-stage samplec. Cluster sampled. Quata sample
192. Why is a census survey not popular?a. It is very costlyb. It takes more timec. It requires large No. of investigators d. All of the above
193. How many different sample of size 3 can be taken from population comprising 5 elements
a. 7b. 12c. 5d. 10
194. Suppose that for a certain population, σ-x is calculated as 30 when a sample size 225 is taken, what would be the value of σ for this infinite population?
a. 500b. 400c. 450d. 600
195. Suppose that a population with N = 200 has µ = 30. What is the mean of the sampling distribution of mean for samples of size 40?
a. 40b. Not possiblec. 25d. 30
196. The precision of proportion as an estimator of the population proportion is the minimum when it is
a. 0.75b. 0.25c. 0.50d. None
197. The standard deviation of a certain population is about 5 units. How large a simple random sample should be of the standard error of the sample mean is to be 1?
a. 25b. 30c. 40d. 60
198. A group of 10 students are to be divided into 2 groups of 5 each and seated at two tables. How many different ways are there of dividing 10 students?
a. 250b. 251c. 252d. 254
199. Find σ-x, If σ = 10, n = 25a. 2b. 4c. 6d. 8
200. Assume that standard deviation (σ) is 300 and n is 25. Calculate standard error of sample mean
a. 40b. 60c. 80d. 100
UNIT 5Estimation
201. A good estimation should bea. Unbiasedb. Consistentc. Efficientd. Sufficiente. All of these
202. Suppose that 160 persons were asked whether they linked a certain TV programme of these 40 persons said they liked it and 120 said they did not like it. Assuming like means a success which of the following is correct?
a. P = 0.75b. P = 0.25c. P = 0.25d. P = 0.33
203. Assuming a sample is taken and its mean is calculated as 240. For a 90% confidence level for µ. The upper limit comes to 280. What is the lower limit of this confidence
a. 220b. 240c. 200d. Cannot be determined
204. For using a t distribution table, which of the following is a necessary condition a. The population is large
b. σ is not known and S is knownc. n is smalld. all of thesee. b and c
205. If the population proportion is not known. The standard error of the proportion can be estimated by using the formula
a. √pq / nb. √npqc. √pq/nd. √npq
206. The Standard deviation of the sampling distribution of a statistic is calleda. Mean errorb. Sampling errorc. Standard deviationd. Standard error
207. Which part of area under the Normal curve is represented by coefficient Z ?a. Right tailb. Left tailc. Both tailsd. None
208. Maximum likelihood estimator of population mean of a Normal distribution isa. xb. n xc. x / nd. None
209. When the sample size is large and Standard deviation is known, then the interval estimate is given by the formula
a. x ± Z Sx
b. x ± Z σ x
c. x ± t σ x
d. x ± t sx
210. Given x = 60, s = 10 and n = 100, then the standard error of sample mean isa. 1.96b. 1c. 10d. None
211. A sampling distribution is the distribution ofa. Meanb. Variancec. Statisticd. Parameter
212. A single number used to estimate an unknown population parameter is a(n) is __________ estimate
a. Pointb. Scalec. Precisiond. None
213. A range of values used to estimate an unknown population parameter a(n) is _____ estimate
a. Pointb. Intervalc. Precisiond. None
214. Once we known something about a sample. The number oif values in the sample we can specify freely is called _______
a. Degree of freedomb. Degree of samplec. Degree of probabilityd. None
215. The family of probability distribution used when the population distribution used when the population standard deviation is unknown, the sample size is small, and the values approximate the Normal is the ___________
a. F testb. Student’s t testc. Z testd. Sample test
216. When we give an interval estimate of a population parameter, we show how sure we are that the Interval contains the actual population parameter by setting a _________ level
a. Intervalb. Binomialc. Confidenced. None
217. The upper confidence Limit and lower confidence limit are the same _________ from the ________
a. Distance, meanb. Distance, Standard deviationc. Distance, mediand. Distance, variance
218. Theoretically, the _______ distribution is the correct distribution to use in constructing confidence intervals to estimate a population proportion.
a. Binomialb. Poissonc. Normald. None
219. In the absence of additional information, a value of ________ should be used for p when determining a sample size for estimating a population proportion
a. P = 0.5b. P = 0.6c. P = 0.4d. P = 0.2
220. Point estimate of population mean is a. µb. µ
c. x
d. X
UNIT 6Testing of Hypothesis
221. When the Null Hypothesis is H0 : µ = 50, then the alternative hypothesis will bea. H1: µ = 49b. H1: µ < 50c. H1: µ ≠ 50d. H1: µ ≥ 50
222. For a Two – Tail test Hypothesis at α = 0.05, the acceptance region isa. b/n Two critical valuesb. outside the two critical valuesc. To left of + ve critical valued. To the right of negative critical value
223. When a null hypothesis is rejected, then it is possible thata. Type III error has been madeb. Correct decisionc. Neither a nor bd. Both a & be. None
224. For a two-tail when n is large the value of Z at 0.05 level of significance isa. 1.645b. 2.58c. 1.96d. None of these
225. Supposing that while testing a hypothesis we think that Type I error will be much costlier than Type II error, which of the following values of α should we adopt?
a. 0.5b. 0.1c. 0.05d. 0.01
226. When α is changed from 0.5 to 1, the probability of rejecting a Null Hypothesis that is actually True
a. Increasesb. Remains samec. Decreasesd. All of these
227. A choice of an appropriate significance level is made by examining the cost ofa. Type II errorb. Type I errorc. Performing the Testd. b and ce. a and bf. a and c
228. When a Test of Hypothesis Involves the mean of a normal population with a known standard deviation, the comparison should be between
a. Observed value of x with critical value of Zb. Observed value of Z with critical value of Xc. The observed value of Z with critical value of Zd. Observed value of X with critical value of Xe. Either c or d
229. Assuming that we want to test whether a population mean is significally smaller or larger than 50, what should be our alternative Hypothesis?
a. µ < 50b. µ > 50c. µ ≠ 50d. Not possible
230. In a hypothesis test, α = 0.05, β = 0.10 the power of test isa. 0.95b. 0.10c. 0.90d. None
231. For testing P1 = P2 is a large sample, the proper test is a. T testb. Z testc. F testd. None
232. Observed x values and critical Z values cannot be compared directly because they are on two different ________
a. Ratingsb. Scalesc. Valuesd. None
233. In order to use the t distribution to test hypothesis about a population mean, we must assume the population is _________ distributed & that its standard deviation is _______
a. Normally, unknownb. Poisson, knownc. Binomial, unknownd. Poisson, unknown
234. To be assured that a hypothesis test is working correctly, we would like the values of 1 – β to be close to ______ as possible
a. 1b. 0c. 0.5d. 0.25
235. The power of test refers to the Test’s ability to _________a. Acceptb. Rejectc. Both a & bd. None
236. The power of test refers to the test’s ability to reject _______ Hypothesisa. Nullb. Alternativec. Both a & bd. None
237. An assumption or speculation made about the value of a population parameter is a _____________
a. Failedb. Unfailedc. Both a & bd. None
238. Accepting a Null Hypothesis, when it is False is a Type ______ errora. Ib. IIc. I & IId. None
239. Rejecting a Null Hypothesis, When it is True is a Type ______ Errora. Ib. IIc. I & IId. None
240. Type I error is denoted by __________a. αb. βc. δd. None
241. Type II error is denoted by __________a. αb. βc. δd. None
242. The assumption about a population parameter that we wish to test is _____Hypothesis
a. Nullb. Alternativec. a & bd. None
243. A hypothesis test involving two rejection regions is called _________a. One - tail testb. Two – tail testc. Both a & bd. None
244. If the Null Hypothesis µ = 10 and the alternative hypothesis µ > 10, then the approximate test to use is a ______ test.
a. Right tailb. Left tailc. Z test
d. t test
245. For any distribution, If n 30, the most approximate test would be _______a. t testb. Z testc. f testd. X2 test
UNIT 7Chi-Square & ANOVA
246. A Chi-square value can Never be Negative becausea. The observed frequencies cannot be –ve b. Difference b/n observed and expected frequencies are squaredc. The sum of differences is computed d. None of these
247. A contingency Table for a chi-square test has 5 columns and 4 rows. How many degree of freedom should be used?
a. 20b. 9c. 15d. 12
248. In a chi-square contingency table, the expected frequency of a cell can be calculated from the expected proportion for the cell by
a. Multiplying Total sample sizeb. Multiplying by Row’s Totalc. Multiplying by column’s Totald. None
249. While performing a chi-square hypothesis we find that several cells have Too small expected frequencies what will be its impact?
a. Degrees of freedom are considerably reducedb. Rejection of Null Hypothesis will be more frequentc. The value of chi-square will be over estimated d. None of thesee. b and c
250. For any given total of significance, the table value of chi-squarea. Declines as degrees of freedom increasesb. Increases as degrees of freedom increasesc. Increases as sample size increasesd. Declines as sample size increases
251. A contingency Table should have frequencies ina. Percentagesb. Mean valuesc. Proportionsd. Frequencies
252. The degree of freedom for a contingency table on the basis of a. N – 1b. C – 1c. R – 1
d. (r – 1) (c – 1)
253. To perform chi-square Testa. Data confirm to a Normal distributionb. Data be measured on a Nominal scalec. Each cell has a equal No. of frequencies d. All of these
254. A contingency Tablea. Always has 2 degrees of freedomb. Always has 2 variablesc. Always has 2 dependent variablesd. All of these
255. The acceptance of Null Hypothesis indicates a. A correct decisionb. Type II errorc. Type I errord. Either a or c
256. In a one-way analysis of variance. The sum of squares is obtained bya. SST – SSBb. SST + SSBc. SSB – SSTd. None of these
257. The F Ratio showsa. Two estimates of population meanb. One estimate of population mean & one estimate of population variancec. Two estimates of population varianced. Both a & ce. None
258. A step in performing ANOVA is to determinea. An estimate of the population variance from among the sample meansb. An estimate of population variance within the samplec. Difference between expected and observed frequency for each classd. a and be. b and c
259. Given n1 = 20, n2 = 15 and a = 0.10 a two tail test in ANOVA is to be performed which of the following represents the upper value to which S12 / S22 should be compared?
260. Any difference among the population means in ANOVA will result into an increased expected value of
a. MSBb. MSWc. MSEd. All of these
261. The degree of freedom between samples for K samples of size n will bea. n – 1b. nk – 1c. k – 1d. none of these
262. The error sum of squares can be obtained fro the equationa. SSE = SSR + SSC – SSTb. SSE = SST + SSR + SSCc. SSE = SST – SSR – SSCd. None of these
263. If the data are displayed in rows & column in a two-way classification, then the degree of freedom will be
a. c – 1b. r – 1c. (r – 1) (c – 1)d. C(r – 1)e. None
264. Which is the assumption of analysis of variance?a. The samples drawn from the population are randomb. The data are quantitative & are normally distributedc. The variance of the population from which samples have been drawn are equald. a and be. a, b and c
265. The mean for the entire group of subjects from all the samples in an experiment is called _______ mean
a. Grandb. Simplec. Multipled. None
266. A statistical technique used to Test the equality of three or more population means is called _________
a. ANOVAb. X2
c. t testd. F test
267. A test of _________ is used to determine whether membership in the categories of one variable is different as a function of membership in the categories of a second variable?
a. Dependenceb. Independencec. ANOVAd. None
268. A family of distributions differentiated by two parameters and used primarily to test hypothesis regarding variances is called _________ distribution
a. tb. Fc. Zd. None
269. The ________ test determines whether there is a significant difference between the observed and hypothesized distributions for a sample
a. Z testb. Goodness – of – fitc. t – testd. poisson
270. Analysis of variance compares the _______ with the ___________ to get ________ statistic
a. Within column variance, b/n C. V, Fb. WCV, BCV, Tc. WCV, BCV, Zd. BCV, WCV, Z
271. The No. of degrees of freedom in the denominator of the F ratio is calculated by subtraction the ___ from the ______
a. No. of samples, TSPb. TSP, No. of samplesc. Random, Integerd. None
For the given problem. It consists of 5 plots and 4 varieties of treatment
272. The value of SST will bea. 4800b. 4236c. 4700d. 4336
273. The value of SSC will bea. 2580b. 2584c. 2586d. 2590
274. The value of SSE will bea. 1670b. 1656c. 1684d. 1693
275. The value of MSC will bea. 860b. 870c. 840d. 855
276. The value of MSE will bea. 102b. 103.5c. 104d. 105.5
277. The degree of freedom between samples isa. 3b. 4c. 5d. 6
278. The degree of freedom within samples isa. 18b. 16c. 19d. 20
279. The value of F test isa. 8.9b. 8.3c. 8.6d. 8.5
280. The table value of F(3, 16) @ 0.05 will be 3.24 So the hypothesis will bea. Acceptedb. Rejectedc. Cannot determined. None
UNIT 8Simple Correlation & Regression
281. While solving a problem, we get an estimating equation Y = 10 – 4x, which of the following indicates this situation
a. Slope of line is negativeb. The Y- intercept of the line is 4c. There is an inverse relationshipd. a and ce. a and b
282. When the regression line of Y on X and the regression line of X on Y from a 900 angle
a. r = ±1b. r = 0c. r = ±05d. None
283. Assuming that after solving a problem you have obtained the regression equation which calculated a is 6 ad b is 3 The problem relates to one dependent & one independent variable. If the dependent variable has a value of 5. What should be the value of dependent variable?
a. 15b. 18
c. 10d. 21
284. Which of the following shows the most correct variation of the Y values around the regression lines
a. Σ Y ( Y – Y )2
b. Σ (Y + Y) 2
c. Σ(Y + ^Y) 2
d. Σ (Y – ^Y) 2
285. When we divide S(Y – Y)2 by S(Y – Y)2 the resultant figure shows:a. Fraction of Total variation in Yb. Fraction of Total variation on account of changes in Xc. Fraction of total variation in Y remains line explainedd. None
286. What will be the range of r when we find that the dependent variable increases as the independent variables increases?
a. 0 – 0.05b. 0 – 2c. 0.1 – 1d. None
287. When 2 regression lines coincide then r isa. 0b. -1c. 1d. 0.5e. None
288. Which of the following is True if the estimating equation has to be a perfect estimator of the dependent variable?
a. The coefficient of determination is -1b. All the data points are on regression linec. The standard error of estimate is zero d. b and ce. a, b and c
289. While testing regression relationship we formulate H0: B = 0 and H1: B1 0. which of the following has to be calculated first to verify H0?
a. Sp
b. Sb
c. Se
d. No. particular order is required
290. Coefficient of determination r2 can be written asa. SST / SSRb. 1 – (SSE / SST)c. SSR / SSTd. b and ce. None
291. Assuming Y as advertising expeditions and X as sales, which is the correct expression of regression of Y on x?
a. (X – X) = r σy (Y – Y) σx
b. (Y – Y) = r (x – x)c. (Y – Y) = r σy (x – x)
σxd. (Y – Y) = σy (x – x)
σx
292. A scatter diagram isa. Statistical testb. Linearc. Curvilineard. A graph showing x & y values
293. Which of the following correlation coefficient shows the Highest degree of association?
a. 0.9b. 0.95c. -0.89d. -1e. 1f. Both d & e
294. Which of the following correlation coefficient shows the lowest degree of association
a. -0.95b. 0.75c. 0.38d. 0.1
295. Which of the following measurement scales is required for the valid calculation of Karl pearson’s correlation coefficient?
a. Ordinalb. Intervalc. Ratiod. Nominal
296. The value of r2 for a particular situation is 0.81 What is the coefficient of correlation
a. 0.81b. 0.9c. 0.09d. None
297. Which of the following is the Highest range of r?a. 0 and 1b. -1 and 0c. -1 and 1d. None
298. When the correlation coefficient between x and y positive. Then as variable x decreases variable Y
a. Remains sameb. Increasesc. Decreases
d. Changes linearly
299. Which of the following measurement scales is required for the valid calculation of spearman correlation coefficient?
a. Ordinalb. Intervalc. Nominald. Ratio
300. Many studies show that advertising expenditure and sales have a high degree of positive association. Which of the following correlation coefficient is consistent with the above statement?
a. – 0.8b. 0.4c. -0.3d. 0.75
Q 301 – 304X 20 16 12 8 4Y 22 14 4 12 8
301. Calculate the value of Σ x2
a. 860b. 870c. 880d. 900
302. The value of Σ XY will bea. 840b. 860c. 880d. 900
303. The value of Σ Y2 will bea. 900b. 900c. 860d. 904
304. The value of r will bea. 0.70b. 0.68c. 0.79d. 0.82
306. Calculate r23.1 if r12 = 0.60a. 0.137b. 0.426c. 0.856
d. 0.921
Q 307 – 310The following results were worked out from scores in statistics & mathematics in a certain examination
(Stat) X (Maths) YMean 40 48Standard Deviation 10 15
307. Find out he value of bxy
a. 0.279b. 0.624c. 0.367d. 0.487
308. Find out the value of byx
a. 0.81b. 0.63c. 0.92d. 0.46
309. Find the value of Y when X = 50a. 54.3b. 59c. 61d. 64
310. Find the value of X when Y = 30?a. 42b. 35.51c. 46d. .48
UNIT 9Business Forecasting & Time series
311. Which of the following components a time series having annual data contains?a. Secular trendb. Cyclical fluctuationc. Seasonal variationd. All of thesee. a and b not c
312. Suppose that a Time series analysis with annual data for 1996 – 2004 gives the equation Y = 20 + 6x + 8x2 on the basis of equation, what is the forecast for 2005?
a. 200b. 250c. 230d. 220
313. Suppose you have a times series data on quarterly basis for 2 years 2003 and 2004. the third quarter of 2004 would be coded as
a. 3b. 5c. 6
d. 7
314. When a time series has an even number of years which are coded, then each coded interval is of
a. One monthb. One yearc. Two yearsd. Six months
315. Which one of the following is not a quantitative method of forecasting?a. Exponential smoothingb. Auto regressive methodc. Input – output analysisd. Delphi – method
316. Which of the following components is used for short – term forecast?a. Cyclicalb. Trendc. Seasonald. None
317. After detrending, a multiplicative model of time series is represented asa. Y = TSIb. Y = TSCIc. Y = TCId. Y = SCIe. None
318. Which of the following methods is used for measuring seasonal variation?a. Method of simple averagesb. Moving average methodc. Ratio to trend methodd. Link, relative methode. All of this
319. Suppose a seasonal index for a particular month is greater than 100. then the following must be True
a. SI for some other month > 100b. SI for some other month = 100c. SI for some other month < 100d. B and ce. None
320. In time series analysis both trends and seasonal variations are studied because they
a. Describe past patternsb. Maximum error of forecastc. Allow the elimination of component from the seriesd. All of the above
321. The standard error of estimate in a forecast using regression analysis, showsa. Time period for which the forecast is validb. Maximum error of forecastc. Overall accuracy of forecastd. All of the above
322. Which of the methods is used to eliminate C from TSCIa. Spearman analysisb. Second – degree analysisc. Relative cyclic residuald. None
323. A Long range forecast implies that the forecast is for the time perioda. At least 1 yearb. Between 1 & 3 yearsc. Broadly 5 & More yearsd. B/n 3 and 5 years
324. Before attempting any time series forecast, one must considera. Extent of accuracy desiredb. Data requiredc. Availability of timed. a and be. a, b and c
325. Which of the following methods is not a subjective method of forecast?a. User’s expectationsb. Jury of executivesc. Box – Jenkins modeld. Delphi method
326. Using seasonal indices to remove effects of seasonality from a time series known as _______ time series
a. Regulatingb. Deseasonalizingc. Trendd. Seasonal
327. The first step in computing the seasonal indices for some times- series data is to calculate the ______
a. Two - quarter moving Totalb. Four - quarter moving Totalc. Three - quarter moving Totald. None
328. The steady increase in the cost of living recorded by CPI is an example of a ______
a. Cyclical trendb. Secular trendc. Seasonal trendd. Irregular trend
329. The result of discarding the highest and lowest values before averaging is called a ________
a. Modified datab. Modified meanc. Modified ranged. Modified median
330. A ___________ is a projection of past patterns into the future
a. Projectb. Forecastc. Estimated. None
UNIT 10Index Numbers
331. If one wants to measure changes in Total monetary worth, then the right choice should be
a. Quantity indexb. Value indexc. Price indexd. None
332. Commodities which show considerable price fluctuations could be best measured by
a. Quantity indexb. Value indexc. Price indexd. None
333. Which of the following can be considered as Normal base period?a. Recent periodb. Remained free from inflation / deflationc. Average of Twod. Neither at peak nor at base
334. Which of the following is used as weights in a quantity index?a. Average of qualitiesb. Percentages of total qualitiesc. Pricesd. None
335. The aggregate price index that uses base year quantities as base isa. Passche’s indexb. Laspeyer’s indexc. Fishers’ indexd. None
336. The two price indices P01 and P10 when multiplied satisfy the following testa. Factor reversal Testb. Time reversal testc. Circular testd. None
337. A time reversal test is satisfied If we usea. Modeb. Arithmetic meanc. Geometric meand. None
338. Which of the following index satisfies circular test?a. Laspreys testb. Paasche’s test
c. Weighted aggregate methodd. None
339. For the three years 95, 96 & 97, the fixed base index nos., were 100, 125 and 150 What would be the chain base index for 1997?
a. 160b. 130c. 120d. 140e. None
340. Which of the following is a quantity index?a. ΣP 1q1 x 100
ΣP0q0
b. ΣP 1q0 x 100ΣP0q0
c. ΣP 0q1 x 100ΣP0q0
d. ΣP 0q1 x 100ΣP1q1
341. Which of the following is the paasche’s price index?a. ΣP 1q0 x 100
ΣP0q0
b. ΣP 1q1 x 100ΣP1q0
c. ΣP 1q1 x 100ΣP0q0
d. ΣP 1q1 x 100ΣP0q1
e. None
342. Which one of the following is the circular test?a. P01 x Q01 = V01
