9.53 Misleading summaries? Two researchers conduct separate studies to test H0: p = 0.50 against Ha: p • 0.50, each with n = 400.

a. Researcher A gets 220 observations in the category of interest, and pn = 220>400 = 0.550 and test statistic z = 2.00. Show that the P@value = 0.046 for Researcher A’s analysis.

b. Researcher B gets 219 in the category of interest, and pn = 219>400 = 0.5475 and test statistic z = 1.90. Show that the P@value = 0.057 for Researcher B’s analysis.

c. Using a = 0.05, indicate in each case from part a and part b whether the result is “statistically significant.”

Interpret.

d. From part

a, part

b, and part

c, explain why important information is lost by reporting the result of a test as

“P@value … 0.05” versus “P@value 7 0.05,” or as “reject H0” versus “do not reject H0,” instead of reporting the actual P-value.

e. Show that the 95% confidence interval for p is

(0.501, 0.599) for Researcher A and (0.499, 0.596) for Researcher B. Explain how this method shows that, in practical terms, the two studies had very similar results.