*15. Given: m 60, s 12. For each of the following scenarios, report za, the sample z ratio, its p value, and the

*15. Given: m ¼ 60, s ¼ 12. For each of the following scenarios, report za, the sample z ratio, its p value, and the corresponding statistical decision. (Note: For a one-tailed test, assume that the sample result is consistent with the form of H1.)

(a) X ¼ 53, n ¼ 25, a ¼ :05 (two-tailed)

(b) X ¼ 62, n ¼ 30, a ¼ :01 (one-tailed)

(c) X ¼ 65, n ¼ 9, a ¼ :05 (two-tailed)

(d) X ¼ 59, n ¼ 1000, a ¼ :05 (two-tailed)

238 Chapter 11 Testing Statistical Hypotheses About m When s Is Known: The One-Sample z Test

(e) X ¼ 54, n ¼ 50, a ¼ :001 (two-tailed)

(f) Why is the 1-point difference in Problem 15d statistically significant, whereas the 5-point difference in Problem 15c is not?