# The IRS is trying to determine which percentage of tax returns claim itemized deductions. A...

## Question:

The IRS is trying to determine which percentage of tax returns claim itemized deductions. A random sample of {eq}2,000 {/eq} returns was taken and the IRS found that {eq}663 {/eq} claimed itemized deductions. Find a large-sample {eq}90\% {/eq} confidence interval based on the sample data.The IRS is trying to determine which percentage of tax returns claim itemized deductions. A random sample of {eq}2,000 {/eq} returns was taken and the IRS found that {eq}663 {/eq} claimed itemized deductions. Find a large-sample {eq}90\% {/eq} confidence interval based on the sample data.

## Confidence Interval:

The confidence interval for the population proportion is constructed by the normal distribution. The normal distribution is a continuous probability distribution. The critical value of the normal distribution is calculated by the excel function *NORMINV()*.

## Answer and Explanation:

Sample size, {eq}n = 2000 {/eq}

Sample proportion, {eq}\hat{p} = \dfrac{663}{2000} = 0.3315 {/eq}

The 90% confidence interval for the population proportion is defined as:

{eq}\hat{p} \pm z_{0.10/2}\times \sqrt{\hat{p}(1-\hat{p})/n} {/eq}

Excel function for the confidence coefficient:

*=NORMINV(0.10/2,0,1)*

{eq}0.3315 \pm 1.645\times \sqrt{0.3315(1-0.3315)/2000}\\ (0.3142, \ 0.3488) {/eq}

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#### Learn more about this topic:

from Statistics 101: Principles of Statistics

Chapter 9 / Lesson 8