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Chapter 7: Q.17 (page 430)

IRS audits The Internal Revenue Service plans to examine an SRS of individual federal income tax returns from each state. One variable of interest is the proportion of returns claiming itemized deductions. The total number of tax returns in each state varies from over 15 million in California to about 240,000in Wyoming.

(a) Will the sampling variability of the sample proportion change from state to state if an SRS of 2000tax returns is selected in each state? Explain your answer.

(b) Will the sampling variability of the sample proportion change from state to state if an SRS of 1%of all tax returns is selected in each state? Explain your answer

Short Answer

Expert verified

a). Yes, the sampling variability will differ from state to state.

b). Yes, the sampling variability will differ from state to state.

Step by step solution

01

Part (a) Step 1: Given Information

The total number of tax returns in each state varies from over 15 million in California to about 240,000 in Wyoming.

02

Part (a) Step 2: Explanation 

Yes, the sampling variability will differ from state to state, because some states will have more variability in the tax returns (more extremely low and more extremely high tax returns) as other states.

03

Part (b) Step 1: Given Information 

The total number of tax returns in each state varies from over 15 million in California to about 240,000 in Wyoming.

04

Part (b) Step 2: Explanation

We take a simple random sample of 2000 tax returns from each state.

The state of California has a larger population than the state of Wyoming.

If the SRS of 2000 students is a larger part of the population, then there will be less sampling variability for the state and thus Wyoming will have less sampling variability than California.

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Most popular questions from this chapter

Suppose that you have torn a tendon and are facing surgery to repair it. The orthopedic surgeon explains the risks to you. Infection occurs in3%such operations, the repair fails in 14%, and both infection and failure occur together 1%at the time. What is the probability that the operation is successful for someone who has an operation that is free from infection?

(a) 0.0767

(b) 0.8342

(c) 0.8400

(d) 0.8660

(e)0.9900

Do you go to church? What sample size would be required to reduce the standard deviation of the sampling distribution to one-third the value you found in Exercise 36 (b)? Justify your answer.

Stop the carl A car company has found that the lifetime of its disc brake pads varies from car to car according to a Normal distrilustion with mean 渭=55000miles and standard deviation蟽=4500miles. The company installs a new brand of brake pads on an SRS of 8cars.

(a) If the new brand has the same lifetime distribution as the previous bye of brake pad, what is the sampling distribution of the mean lifetime x?

(b) The average life of the pads an these 8cars turns out to be x=51800miles. Find the probability that the sample mean lifetime is 51800miles or less if the lifetime distribution is unchanged, What conclusion would you draw?

The central limit theorem is important in statistics because it allows us to use the Normal distribution to make inferences concerning the population mean

(a) if the sample size is reasonably large (for any population).

(b) if the population is normally distributed and the sample size is reasonably large.

(c) if the population is normally distributed (for any sample size).

(d) if the population is normally distributed and the population variance is known (for any sample size).

(e) if the population size is reasonably large (whether the population distribution is known or not,

Doing homework Refer to Exercise 9.

(a) Make a graph of the population distribution given that there are 3000 students in the school. (Hint: What type of variable is being measured?)

(b) Sketch a possible graph of the distribution of sample data for the SRS of size 100 taken by the AP Statistics students.
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