Question

3.1.18 Suppose we are constructing a confidence interval using repeated tests of significance to develop an interval of plausible values. Using two- sided tests each time with the following null hypotheses, we obtain the resulting p-values. Null p-value Null p-value Proportion = 0.45 0.014 Proportion = 0.53 Proportion = 0.46 0.032 Proportion = 0.54 Proportion = 0.47 Proportion = 0.48 Proportion = 0.49 Proportion = 0.50 Proportion = 0.51 Proportion = 0.52 0.062 0.126 0.371 0.598 0.733 0.986 Proportion = 0.55 Proportion = 0.56 Proportion = 0.57 Proportion = 0.58 Proportion = 0.59 Proportion = 0.60 0.787 0.572 0.373 0.142 0.077 0.042 0.021 0.003 a. Using the results from the table, give a 90% confidence interval. b. Using the results from the table, give a 95% confidence interval.

Answer 1

a.

For 90% confidence interval,  $\alpha$ = (1 - 0.9)/2 = 0.05

The p-value should be near to 0.05,

Using the table, 90% confidence interval is,

(0.47, 0.58)

b.

For 95% confidence interval,  $\alpha$ = (1 - 0.95)/2 = 0.025

The p-value should be near to 0.025,

Using the table, 95% confidence interval is,

(0.46, 0.59)