Question: Given \({{H}_{0}}\) : µ = 53.1 and \({{H}_{1}}\) : µ < 53.1 with observed sample mean \(\bar{X}\) = 52.7, sample standard deviation s = 4.5, and a sample size n = 40. Use \(\alpha =0.01\)

(a) Convert the sample mean \(\bar{X}\) to a sample z value. (Hint: due to the large sample size, approximate σ with s.)

(b) Sketch a graph of the z distribution. Show the location of the area corresponding to the P value for this test.

(c) Compute the P value for this test.

(d) Is the data significant at the specified level of significance \(\alpha =0.01\) ?