Statistics and Mechanics mock 2

Statisitics 50 marks

Mechanics 50 marks

2 Hours

Name____________

1) Jo, Suki and Amin are discussing where in the UK had the best average daily temperature in 1987. They each took a sample from the place that they thought had the highest mean temperature. The sample data is below.

Hurn 1987Date 08/05/1987 03/09/1987 07/08/1987 30/07/1987 30/06/1987 07/07/1987 21/09/1987 10/06/1987

Temp

8.1 18.4 12.4 15.5 17.8 20.4 17.6 9.2

Leeming 1987

Date 03/06/1987 04/06/1987 05/06/1987 06/06/1987 07/06/1987 08/06/1987 09/06/1987 10/06/1987Temp

11.4 10.9 9.4 12.2 12.1 10.3 10.3 10.6

Heathrow 1987

Date 01/05/1987 02/05/1987 01/06/1987 02/06/1987 01/07/1987 02/07/1987 01/08/1987 02/08/1987Temp

14.6 8.8 15.4 13.7 16.1 16.6 17.5 17.4

a) Why might Jo and Amin criticise Suki’s Leeming sample? (1 mark)b) Suggest what sampling method was used for each of the Hurn and Heathrow samples, and give one

advantage and one disadvantage for each method. (2 marks)c) Amin claims that Heathrow has the highest average mean. Without further calculation, suggest why Amin

cannot be sure about his claim. (1 mark)d) Despite the inaccuracy of the test, why would you expect Amin’s claim to be correct. (1 mark)e) Upon further investigation, Suki finds that the sample mean temperature in Leeming is 11.025, and the

median is 10.75. She decides that the daily average temperature in Leeming could be measured using a normal distribution. Give a reason to support Suki’s claim. (1 mark)

2)

Priya’s teacher has suggested that there is a relationship between the number of hours spent revising and the number of marks scored in an exam. Priya decides to investigate her teacher’s claim by recording her classmates’ marks against how many hours of revision they claimed to have done. The results are below.

Hours 3 4 0 7 9 15 2 1Test score % 60 60 45 95 85 80 35 40

a) Use your calculator to work out the correlation coefficient between the amount of hours spent revising and the test score

(2 marks)b) Test, at the 2.5% level of significance, Priya’s teacher’s claim. State your hypotheses clearly.

(4 marks)c) Use you calculator to find an equation for a regression line in the form y=ax+b. Making sure that y is the

dependent variable(3 marks)

d) In context, what do the values a and b tell you?(2 marks)

e) Isabelle looks at Priya’s data and decides that she will do 20 hours of revision. Explain why Priya’s model does not apply to Isabelle.

(1 mark)

3) In Leuchars, between May and October inclusive, it rained on 65 out of 184 days. Josh suggests using a binomial distribution to model the number of days of rain in Leuchars over this time.

a. State, with two reasons, whether or not a binomial model is a sensible idea(1 marks)

b. Using the binomial model, how many days of rain would you expect in a 30 day month(2 marks)

c. By applying the same model to the same period, May-October, of the following year, what is the probability of there being between 30 and 70 rainy days inclusive.

(2 marks)

Sasha claims that this binomial model can be approximated using a normal distribution

d. Explain why Sasha’s claim is correct(1 mark)

e. Use the normal distribution as an approximation for the binomial distribution to find the probability of there being between 60 and 70 (inclusive) rainy days in a 184 day period.

(4 marks)f. Find the percentage difference between the binomial calculation and the normal approximation.

(2 marks)

During a 2 week period in Leeming, there are 9 days with rain. Alexa claims that Leeming must have a different proportion of rainy days to Leuchars.

g. Using a Binomial model, and a 5% significance level, test whether Alexa’s claim is correct. State your hypotheses clearly.

(3 marks)

4)

a) Draw a Venn diagram to illustrate the above information(4 marks)

( 2)

5)

The following week Paul feels unwell, he still trains every day, but thinks he does less exercise. His sample mean for the week was 80 minutes.

c) Test, at the 5% significance level, whether Paul’s claim is correct.

(4 marks)

6)

a) Find the initial horizontal and vertical speed of the ball(4 marks)

(b)

(6 marks)

7)

8)

9)

(4)

10)