9.55 Effect of n Example 10 analyzed political conservatism and liberalism in the United States. Suppose that the sample mean of 4.09 and sample standard deviation of 1.43 were from a sample size of only 25, rather than 2449.

a. Find the test statistic.

b. Find the P-value for testing H0: m = 4.0 against Ha: m • 4.0. Interpret.

c. Show that a 95% confidence interval for m is (3.5, 4.7).

d. Together with the results of Example 10, explain what this illustrates about the effect of sample size on

(i) the size of the P-value (for a given mean and standard deviation) and (ii) the width of the confidence interval.