Chapter 9.5, Problem 53PB

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

1. a. Researcher A gets 220 observations in the category of interest, and $\hat{p}=220/400=0.550$ and test statistic z = 2.00. Show that the P-value = 0.046 for Researcher A’s analysis.
2. b. Researcher B gets 219 in the category of interest, and $\hat{p}=219/400=0.5475$ and test statistic z = 1.90. Show that the P-value = 0.057 for Researcher B’s analysis.
3. c. Using α = 0.05, indicate in each case from part a and part b whether the result is “statistically significant.” Interpret.
4. 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 > 0.05,” or as “reject H₀” versus “do not reject H₀,” instead of reporting the actual P-value.
5. 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.