Discuss the below:
Q: An automaker tests the accuracy of speedometers purchased from a vendor on a weekly basis. The test plan calls for testing a random sample of 25 speedometers at a nominal speed of 55 mph. A statistically significant deviation at 1% significance level from the nominal value results in rejection of the lot supplied by the vendor. Two successive rejections call for re-qualification of the vendor.
a) Let mu be the mean speed indicated by the speedometers when the testing apparatus is set at the nominal speed of 55 mph. Set up the hypotheses for doing the test. Explain the rationale for setting up the hypotheses.
b) Suppose that in a particular test, the sample mean reading for the tested speedometers was 56.5 mph and the sample SD of the readings was 2.5 mph. Is this significant evidence to suggest that the mean reading deviates significantly from the nominal value of 55 mph at the 1% significance level?Calculating the P-value.