Competitors in the 'under 16' age group think the triathlon course was particularly difficult compared with previous events and so the mean time to complete this event was slower than usual. They claim that the population mean time to complete the triathlon for the under 16 age group is 59.5 minutes.

(a) Write down suitable null and alternative hypotheses to test the theory that the population mean time for under 16's to complete the triathlon is 59.5 minutes. State clearly the meaning of any symbols that you use.

(b) Carry out a one-sample t-test to test the hypotheses that you wrote down in part (a).

In your answer, make sure to include the following:

- the estimated standard error

- the value of the test statistic

- the p-value or the values of CV5

- what conclusions can be drawn from the results of this test.

(c) Calculate by hand the 95% confidence interval for the population mean time taken for under 16s to complete the triathlon based on the t-test. Show your working.

(d) Would a 90% confidence interval for the population mean time taken for under 16s to finish the triathlon be wider or narrower than the 95% confidence interval that you calculated in part (c).

TIMES

67.33 70.40 61.63 70.12 71.15 62.67 67.80 71.67 55.43 56.14 59.48 53.03