Calculation practice: Confidence interval for a population proportion. In a study in Scotland (as reported by Devlin 2009), researchers left a total of 240 wallets around Edinburgh, as though the wallets were lost. Each contained contact information including an address. Of the wallets, 101 were returned by the people who found them. With the following steps, use the data to estimate the proportion of lost wallets that are returned, and give a 95% confidence interval for this estimate.

a. What is the observed proportion of wallets that were returned?

b. Calculate p' to use in the Agresti–Coull method of calculating a 95%

confidence interval for the population proportion.

c. Calculate the lower bound of the 95% confidence interval.

d. Calculate the upper bound of the 95% confidence interval.

e. Provide two values for P^P that lie within the most-plausible range, according to these data, and two that lie outside.

f. If the authors had tested the null hypothesis that p^p. was 1/21/2 at a significance level 0.05, is it likely that they would have rejected the null hypothesis (base your answer only on your results above)?