Recall that it is hoped that the mean alert time, m, using the new display panel is less than eight seconds.
(1) Formulate the null hypothesis H0 and the alternative hypothesis Ha that would be used to attempt to provide evidence that m is less than eight seconds.
(2) Discuss the meanings of a Type I error and a Type II error in this situation.
(3) The mean and the standard deviation of the sample of 15 alert times are 7.4 and 1.0261, respectively. Test H0 versus Ha by setting α equal to .05 and using a critical value. Assume that the population of all alert times using the new display panel is approximately normally distributed.
(4) Interpret the p- value of .02 for the test.