Reference no: EM132529346

Suppose a research believes that the mean age of all race car drivers is greater than 30 years. To test this claim, she randomly sampled 11 drivers and obtained the ages in years as follows:

32

28

24

33

33

41

33

34

40

27

30

Use a 5% level of significance to test her claim, assuming the ages of all race car drivers are normally distributed.

The sample data give a mean of 32.27 and a standard deviation of 5.1.

(i) Draw a fully labelled box plot of these data. Show your workings. (You may assume there are no outliers and therefore it is NOT necessary to calculate upper and lower fences.)

(ii) Write down the null and alternative hypotheses for the test to determine whether the mean age of all race car drivers is greater than 30 years.

(iii) Write down the calculation needed to find the test statistic for the test in (ii), including the formula used. (You do NOT need to work this out.)

(iv) Find the critical value(s) to use in the test in (ii) using a = 0.05.

(v) The test statistic is calculated as 1.48 (2 d.p.), what is the statistical decision using a = 0.05? Explain in a sentence.

(vi) Explain in a sentence what the conclusion for the test in part (ii) would be using a = 0.05.

(vii) What level of confidence would we need to use if we wanted to calculate the related confidence interval to support the test in (ii) using a = 0.05?

(viii) The confidence interval in (vii) was calculated as (29.48, 35.06). Explain in a sentence what further information this gives in relation to the test in (ii).