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 p̂ = 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 α = 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.