14.33 A test goes wrong. Software can generate samples from (almost) exactly Normal distributions. Here is a random sample of size 5 from the Normal distribution with mean 10 and standard deviation 2:

6.47 7.51 10.10 13.63 9.91 These data match the conditions for a ?: test better than real data will: the population is very close to Normal and has known standard deviation a =1, and the population mean is /r, = 10.

Test the hypotheses Hq: IX = 8 H,: M 7^ 8

(a) What are the z statistic and its P -value? Is the test signif icant at the 5% level?