In a recent study involving the Internal Revenue Service IRS

In a recent study involving the Internal Revenue Service (IRS), information was gathered on the IRS\'s ability to provide correct answers to ta questions asked over the phone. Based on sample information, a 95% confidence interval for p, the true proportion of phone calls in which the IRS provided correct answers was (0.81, 0.89)

a. What was the value of the sample proportion used to construct the interval?

b. For a future study, how many phone calls should be monitored in order to estimate p to within one percent with 95% confidence?

c. Give a written interpretation of the 95% confidence interval for p.

Solution

a. What was the value of the sample proportion used to construct the interval?

sample proportion= (0.81+0.89)/2 = 0.85

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b. For a future study, how many phone calls should be monitored in order to estimate p to within one percent with 95% confidence?

Given a=1-0.95=0.05, Z(0.025) = 1.96 (from standard normal table)

So n=(Z/E)^2*p*(1-p)

=(1.96/0.01)^2*0.85*(1-0.85)

=4898.04

Take n=4899

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c. Give a written interpretation of the 95% confidence interval for p

We have 95% confident that the population proportion will be within this interval.