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Chapter 7: Q.23 (page 431)

If we take a simple random sample of size n=500from a population of size 5,000,000, the variability of our estimate will be

(a) much less than the variability for a sample of size n=500 from a population of size 50,000,000.

(b) slightly less than the variability for a sample of size n=500from a population of size 50,000,000.

(c) about the same as the variability for a sample of size n=500from a population of size 50,000,000.

(d) slightly greater than the variability for a sample of size n=500from a population of size 50,000,000.

(e) much greater than the variability for a sample of size n=500 from a population of size 50,000,000.

Short Answer

Expert verified

A correct answer is an option (C) about the same as the variability for a sample of size n=500 from a population of size 50,000,000.

Step by step solution

01

Given Information

A simple random sample of size n=500 from a population of size 5,000,000,

02

Explanation

A simple random sample is expected to have roughly the same variability as its population and thus answer (c) is correct.

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Most popular questions from this chapter

About 75%of young adult Internet users (ages 18 to 29) watch online video. Suppose that a sample survey contacts an SRS of 1000 young adult Internet users and calculates the proportion p^in this sample who watch online video.

4. If the sample size were 9000 rather than 1000 , how would this change the sampling distribution of p^?

A grocery chain runs a prize game by giving each customer a ticket that may win a prize when the box is scratched off. Printed on the ticket is a dollar value (\(500,\)100,\(10)or the statement, 鈥淭his ticket is not a winner.鈥� Monetary prizes can be redeemed for groceries at the store. Here are the distribution of the prize values and the associated probabilities for each prize:

Which of the following are the mean and standard deviation, respectively, of the winnings?
\)15.00,\(2900.00
(b) \)15.00,\(53.85
(c) \)15.00,\(26.9

(d) \)156.25,\(53.85

(e) \)156.25,$26.93

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

Doing homework A school newspaper article claims that 60%of the students at a large high school did all their assigned homework last week. Some skeptical AP Statistics students want to investigate whether this claim is true, so they choose an SRS of 100students from the school to interview. What values of the sample proportion p藛 would be consistent with the claim that the population proportion of students who completed all their homework is p 0.60? To find out, we used Fathom software to simulate choosing 250SRSs of size n=100students from a population in which p=0.60. The figure below is a dotplot of the sample proportion p藛of students who did all their homework.

(a) Is this the sampling distribution of p藛? Justify your answer.

(b) Describe the distribution. Are there any obvious outliers?

(c) Suppose that 45of the100students in the actual sample say that they did all their homework last week. What would you conclude about the newspaper article鈥檚 claim? Explain.

In a certain large population of adults, the distribution of IQ scores is strongly left-skewed with a mean of 122and a standard deviation of 5. Suppose adults are randomly selected from this population for a market research study. The distribution of the sample mean of IQ scores is

(a) left-skewed with a mean of 122and a standard deviation of 0.35.

(b) exactly Normal with mean 122and standard deviation 5.

(c) exactly Normal with mean 122and standard deviation 0.35.

(d) approximately Normal with mean122and standard deviation 5.

(e) approximately Normal with a mean122and standard deviation0.35.
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