Example 11 analyzed political conservatism and liberalism in the United States. Suppose that the sample mean of 4.11 and sample standard deviation of 1.43 were from a sample size of only 25, rather than 1933.
a. Find the test statistic.
b. Find the P-value for testing H0: μ = 4.0 against Ha: μ ≠ 4.0. Interpret.
c. Show that a 95% confidence interval for μ is (3.5, 4.7).
d. Together with the results of Example 11, 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.

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