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 z test better than real data will: the population is very close to Normal and has known standard deviation σ = 2, and the population mean is μ = 10. Test the hypotheses H0: μ = 8 Ha: μ = 8

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

(b) We know that the null hypothesis does not hold, but the test failed to give strong evidence against H0. Explain why this is not surprising.