MB0040

Master of Business Administration- MBA Semester 1 Reg No.: 511011932

MB0040 – Statistics for Management - 4 Credits

Assignment Set- 1 (60 Marks)

Q1. Elucidate the functions of statistics.

Functions or Uses of Statistics

(1) Statistics helps in providing a better understanding and exact description of a

phenomenon of nature.

(2) Statistical helps in proper and efficient planning of a statistical inquiry in any field of

study.

(3) Statistical helps in collecting an appropriate quantitative data.

(4) Statistics helps in presenting complex data in a suitable tabular, diagrammatic and

graphic form for an easy and clear comprehension of the data.

(5) Statistics helps in understanding the nature and pattern of variability of a

phenomenon through quantitative observations.

(6) Statistics helps in drawing valid inference, along with a measure of their reliability

about the population parameters from the sample data.

Q2. What are the methods of statistical survey? Explain briefly.

Statistical surveys are used to collect quantitative information about items in a

population. Surveys of human populations and institutions are common in political polling

and government, health, social science and marketing research. A survey may focus on

opinions or factual information depending on its purpose, and many surveys involve

administering questions to individuals. When the questions are administered by a

researcher, the survey is called a structured interview or a researcher-administered

survey. When the questions are administered by the respondent, the survey is referred

to as a questionnaire or a self-administered survey. Methods used to increase response

rates

brevity - single page if possible

financial incentives

paid in advance

paid at completion

non-monetary incentives

commodity giveaways (pens, notepads)

SIKKIM MANIPAL UNIVERSITY DISTANCE EDUCATION 1


entry into a lottery, draw or contest

discount coupons

promise of contribution to charity

preliminary notification

foot-in-the-door techniques - start with a small inconsequential request

personalization of the request - address specific individuals

follow-up requests - multiple requests

claimed affiliation with universities, research institutions, or charities

emotional appeals

bids for sympathy

convince respondent that they can make a difference

guarantee anonymity

legal compulsion (certain government-run surveys)

Sampling

Main article: Sampling (statistics)

Sample selection is critical to the validity of the information that represents the

populations that are being studied. The approach of the sampling helps to determine the

focus of the study and allows better acceptance of the generalizations that are being

made. Careful use of biased sampling can be used if it is justified and as long as it is

noted that the resulting sample may not be a true representation of the population of the

study. There are two different approaches to sampling in survey research:

There is nonprobability sampling approach. In this approach the researcher does not

know each element's probability of selection in the sample. The most commonly used

nonprobability sampling method is the convenience sampling approach. With this

method, it only samples those who are available and willing to participate in the survey.

The use of this approach allows for convenience for the researcher while possibly losing

data validity due to the lack of representation.

The probability sampling approach for research methods gives each element a known

chance of being included in the sample. This method is closer to a true representation of

the population. It can be difficult to use due to cost of a rigorous sampling method, and

difficulty in obtaining full coverage of the target population, but the generalizations that

come from it are more likely to be closer to a true representation of the population.



Different forms of probability sampling are designed to achieve various benefits - e.g.

theoretical simplicity, operational simplicity, detailed information on subpopulations, or

minimal cost. Some common forms:

Equal probability of selection designs (EPS), in which each element of the population

has an equal chance of being included in the sample. This uniformity makes EPS

surveys relatively simple to interpret. Forms of EPS include Simple random sampling

(SRS) and systematic sampling.

Probability-proportional-to-size designs (PPS), in which 'larger' elements (according to

some known measure of size) have a higher chance of selection. This approach is

common in business surveys where the object is to determine sector totals (e.g. "total

employment in manufacturing sectors"); compared to EPS, concentrating on larger

elements may produce better accuracy for the same cost/sample size.

Stratified random sampling approach, in which the population is divided into

subpopulations (called strata) and random samples are then drawn separately from each

of these strata, using any probability sampling method (sometimes including further sub-

stratification). This may be done to provide better control over the sample size (and

hence, accuracy) within each subpopulation; when the variable/s of interest are

correlated with subpopulation, it can also improve overall accuracy. Another use for

stratification is when different subpopulations require different sampling methods - for

instance, a business survey might use EPS for businesses whose 'size' is not known

and PPS elsewhere.



Q3.Tabulate the following data:

Age: 20-40; 40-60;60-above

Departments: English, Hindi, Political science, History, sociology

Degree level: Graduates, Post graduates; PhD,

Total students in age group and in degree level.

AGE DEPARTMENT DEGREE

20-40

E, H, P, S, H, Socially

English, History

Graduates/Post

Graduate/PHD

By Post Graduate

40-60 All the student Great with PhD

60-above Compulsory With the Degree

A statistical table is a systematic organization of data in Row & Column. According to

prefers Connor tabulation involves an orderly & systematic presentation of numerical

data in a form design to complain the problem under consideration.

(i) table No:- Ist of all a table must be numbered different tables must have different no.

numbers help location of the table.

(ii) Titles:- A table must have a title, title must be written in board latters.

(iii) Head notes:- If the title of table does not give complete information. Its sample

mented with the head notes.

(iv) Stubs:- stubs are titles of the Row’s of the table

(v) Caption:- Caption is the title given to the column’s of the table.

Q4. The data given below is the distribution of employees of a business according

to their efficiency. Find the mean deviation and coefficient of mean deviation from

Mean and Median:

Efficiency Index 22-26 26-30 30-34 34-38 38-42

Emloyees 25 35 15 5 2



Efficiency

Index

Employees

F

x fx F(x-

median)

22-26 25 24 600 -4.29 107.25 8 200

26-30 35 28 980 -.29 10.15 4 140

30-34 15 32 480 3.71 55.65 0 0

34-38 5 36 180 7.71 38.55 4 20

38-42 2 40 80 11.71 23.42 8 16

82 2320 235.02 24 376

= 0.10

Q5. What is conditional probability? Explain with an example.

Conditional probability is the probability of some event A, given the occurrence of some

other event B. Conditional probability is written P(A|B), and is read "the (conditional)

probability of A, given B" or "the probability of A under the condition B". When in a

random experiment the event B is known to have occurred, the possible outcomes of the

experiment are reduced to B, and hence the probability of the occurrence of A is

changed from the unconditional probability into the conditional probability given B.

Joint probability is the probability of two events in conjunction. That is, it is the probability

of both events together. The joint probability of A and B is written or



Marginal probability is then the unconditional probability P(A) of the event A; that is, the

probability of A, regardless of whether event B did or did not occur. If B can be thought

of as the event of a random variable X having a given outcome, the marginal probability

of A can be obtained by summing (or integrating, more generally) the joint probabilities

over all outcomes for X. For example, if there are two possible outcomes for X with

corresponding events B and B', this means that . This is called marginalization.

In these definitions, note that there need not be a causal or temporal relation between A and B. A may precede B or vice versa or they may happen at the same time. A may cause B or vice versa or they may have no causal relation at all. Notice,

Q6.The probability that a football player will play Eden garden is 0.6 and on Ambedkar Stadium is 0.4. The probability that he will get knee injury when playing in Eden is 0.07 and that in Ambedkar stadium is 0.04.What is the probability that he would get a knee injury if he played in Eden.

P (E1) = 0.6 P(E2) = 0.4

A be the engree (AE1) = 0.07

P (A / E2) = -

= 0.3



MB0040 – Statistics for Management - 4 Credits

Assignment Set- 2 (60 Marks)

Q1. A random sample of 6 sachets of mustard oil was examined and two were found to be leaking. A wholesaler receives seven hundred twenty six packs, each containing 6 sachets. Find the expected number of packets to contain exactly one sachet leaking?Sol.

N = 6P = 2H = 4

Total no, of outones = 726P (x =1) c (n1r) Pr q n-r

C (6, 1) P1 q5

6 x 726 x 1= 4356

Q2. What do you mean by errors in statistics? Mention the measures to do so.

The standard error of a method of measurement or estimation is the standard deviation

of the sampling distribution associated with the estimation method. The term may also

be used to refer to an estimate of that standard deviation, derived from a particular

sample used to compute the estimate.

For example, the sample mean is the usual estimator of a population mean. However,

different samples drawn from that same population would in general have different

values of the sample mean. The standard error of the mean (i.e., of using the sample

mean as a method of estimating the population mean) is the standard deviation of those

sample means over all possible samples (of a given size) drawn from the population.

Secondly, the standard error of the mean can refer to an estimate of that standard

deviation, computed from the sample of data being analysed at the time.

The term standard error is derived[citation needed] from the fact that, as long as the

estimator is unbiased, the standard deviation of the error (the difference between the



estimate and the true value) is the same as the standard deviation of the estimates

themselves; this is true since the standard deviation of the difference between the

random variable and its expected value is equal to the standard deviation of a random

variable itself.

In many practical applications, the true value of the standard deviation is usually

unknown. As a result, the term standard error is often used to refer to an estimate of this

unknown quantity. In such cases it is important to be clear about what has been done

and to attempt to take proper account of the fact that the standard error is only an

estimate. Unfortunately, this is not often possible and it may then be better to use an

approach that avoids using a standard error, for example by using maximum likelihood

or a more formal approach to deriving confidence intervals. One well-known case where

a proper allowance can be made arises where the Student's t-distribution is used to

provide a confidence interval for an estimated mean or difference of means. In other

cases, the standard error may usefully be used to provide an indication of the size of the

uncertainty, but its formal or semi-formal use to provide confidence intervals or tests

should be avoided unless the sample size is at least moderately large. Here "large

enough" would depend on the particular quantities being analysed.

Q3. From a population known to have a standard deviation of 1.4, a sample of 70 individuals is taken. The mean of this sample is found to be 6.2. Find the standard error of the mean. Also establish an interval estimate around the sample mean using one standard deviation of the mean.Sol. Standard error of mean (i) When standard deviation of the population is know

refers to the standard error of the mean

p standard deviation of the the populationN = number of observation

0.5645



Q4. A machine is designed so as to pack 300ml of a solution with a standard deviation of 5ml. A sample of 150 bottles when measured had a mean content of 201.3ml. Test whether the machine is functioning properly.(use 5% level of significance)

Q5. Out of 2000 people surveyed, 1200 belong to urban areas and rest to semi urban areas. Among 1000 who visited other regions, 800 belonged to urban areas. Test at 5% level of significance whether area and visiting other states are dependant.



199.31

1.6551

Q6. How is statistics useful for modern managers? Give examples and explain.

Managers need an understanding of statistics for four key reasons: to know how to

properly present and describe information; to know how to draw conclusions about large

populations based only on information obtained from samples; to know how to obtain

reliable forecasts and to know how to improve processes . These four reasons form the

basis of the structure and content of Statistics for Managers. There is not a single activity

undertaken in business or in everyday life that does not involve probability. In many

cases the probabilities are consciously considered while in others they may be

subconscious. Ordering a particular level of stock for a retail outlet involves a probability

consideration of the actual demand for the products. Undertaking tertiary studies

involves probability estimations for levels of future income that a degree will produce. In

the same way, almost all business decisions depend on probability evaluation. It is

important then for you to have an understanding of probability analysis.

Having developed our basic ‘feel’ for probabilities we need to develop an understanding

of the key theoretical probability distributions. These enable us to assign probabilities of

all potential outcomes for a given situation. This work will enable us to move onto the

very important statistical concept called the sampling distribution. Many data sets for the

business manager are samples drawn from a wider population. Of interest to the

manager are the conclusions that can be drawn about the relevant population

characteristic from the sample statistic. We might have some market research that

indicates that customer acceptance of a new brand is 30%. The obvious conclusion is

that 30% of all potential customers will accept the brand. However, if the sample is not

representative of the population then the results may be misleading. Even when the



sample is representative, intuitively we would not believe that exactly the same result

would hold for the population. We need to understand how samples are taken from

population and what affect this has on sample statistics such as the sample mean,

sample proportion etc. We will examine sampling theory and the resulting sampling

distributions. These are probability distributions for sampling situations.

The idea of sampling in business situations and inferential statistics as a method for

drawing conclusions about population parameters from sample statistics are both

fundamental issues in statistics. The problem with a sample, however, is error. A sample

is unlikely to be an accurate representation of the whole population but the concept of

the confidence interval can be used to cope with sample error.

1. The six sigma is the best way in managing the business which puts all the data and

while using the data and facts in order to have a better solution. This can also be use for

the improvement of the customer satisfaction, to reduce the time of the cycle, and can

also reduce the defects.

a). The control chart for the product and service of Brecker Associates, Inc. First Phase

Quantifying Opportunities

Second Phase

Planning Solutions

Third Phase

Re-designing

Process

Fourth Phase

Implementing Change

Performance Data Planning Solutions

b.) The techniques in valuing are the ways that the business is using for the productivity

of the business and the process, the cost and the quality. This includes the company’s

workshop on design, marketing, quality, operations, purchasing and the personnel

supplier. In this manner, the first phase is the quantification of the opportunities of

Brecker Associates Inc. which use for the quantification and determination of the

services and products that the company is producing. For the planning solution which is

the second phase is the move or the way that the company had been notified in order to

get solutions for the circumstances in the company. The designing again of the plan is

also applicable as for the improvement of the company’s services and products. The



implementation of the change is applicable after the exact analyzation and detailed

outcome of the plan. With the aide of the QFD technique, the requirements for the

customer can be determined and can also be quantified. This way, the benefits

regarding the improvements had been sought and identified and are being refined for the

improvement of the services. These can also lead to the redesign of the products which

was the company’s phase 3. The redesigned of the specified components or the

processes are charged and made an additional tools and quality that had been used for

the design in the manufacture, in lean thinking, the design of the assembly, and the

reduction set-up. These phases are all dependent on the data planning solutions

performance.

The processes are in control of the team which only signifies that the results are all at

the hands of the team.

c). The recommended policy is to have a keen understanding of the team towards the

required factors which can improve the performance of the products and services as

benefitted to the employees and to the company.

7. The scatter diagram of the given data is given below. Based on the graph, the data

are interrelated to one another which only show that the weight of the mails has high

correlation to the number of orders. Computing the relationship of the mails’ weight and

the number of orders it will get the value of the Pearson r or the correlation coefficient to

be 0.99 and interpreted as high correlation.

a). Using the least-square method the regression line had been notified and

approximately as y = 5.55 + 32.76x. This means that the slope is 32.76 with the vertical

intercept to be 5.55.

b). This means that whatever the value to be substituted in x will always depend on the

slope and to the vertical intercept so that it can get the value of y or the weight of the

mails.

c). Using the regression line, substitute the value of weight of the mails in y or 500

pounds. The value of x got is 15.0931 or $15,093.10.

d). The prediction is reliable because it use the regression line and the value that had

got is near to the least square regression line.


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