Question:

(a) Suppose that 100 tires made by Bridgestone last on average 21,819 miles with a standard deviation of 1,295 miles. Test the null hypothesis µ = 22, 000 miles against the alternative hypothesis µ < 22, 000 miles at the 5% level of con?dence.

(b) It is decided that H0 is rejected if the sample mean is less than 21,819. Using the same information in part (a) above, except for the 5% level of con?dence, calculate

(i) P(H0 is accepted | H1 is true with µ = 21, 500).
(ii) the power of the test.

(c) The results of 100 students who have taken part in examinations on Probability and Statistics during the past few years can be summarised as follows. Out of 42 males, 30 have passed and out of 58 females, only 34 have passed. Test at the 5% signi?cance level whether there is a relationship between gender and success in modules of Probability and Statistics.