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Chapter 7: Q. T7.8 (page 438)

Which of the following statements about the sampling distribution of the sample mean is incorrect?

a. The standard deviation of the sampling distribution will decrease as the sample size increases.

b. The standard deviation of the sampling distribution measures how far the sample mean typically varies from the population mean.

c. The sample mean is an unbiased estimator of the population mean.

d. The sampling distribution shows how the sample mean is distributed around the population mean.

e. The sampling distribution shows how the sample is distributed around the sample mean.

Short Answer

Expert verified

(e). The sampling distribution is incorrect because it is the distribution of all possible sample means, which cannot be centred on the sample mean.

Step by step solution

01

Given Information

The choices are,

a. As the sample size grows, the sampling distribution's standard deviation decreases.

b. The sampling distribution's standard deviation indicates how far the sample mean normally differs from the population mean.

c. The sample mean is a reliable predictor of the population average.

d. The sampling distribution depicts the distribution of the sample mean around the population mean.

e. The sampling distribution depicts the distribution of the sample around the sample mean.

02

Explanation for correct option

a. Yes, because a bigger sample size provides more information about the population and so allows for more precise forecasts.

b. Correct, the variability of the sample mean over all potential samples is the standard deviation of the sampling distribution of the sample mean.

c. Yes, the sample mean is a reliable predictor of the population mean.

d. Correct, because the variation is determined by the sample distribution's standard deviation.

Because the sampling distribution represents the distribution of all potential sample means, it cannot be centred on the sample mean. e. Incorrect.

As a result, the best solution is (e)

03

Explanation for incorrect option

a. The standard deviation of the sampling distribution will decrease as the sample size increases is not the answer.

b. The standard deviation of the sampling distribution measures how far the sample mean typically varies from the population mean is not the answer.

c. The sample mean is an unbiased estimator of the population meanis not the answer.

d. The sampling distribution shows how the sample mean is distributed around the population mean is not the answer.

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Most popular questions from this chapter

An insurance company claims that in the entire population of homeowners, the mean annual loss from fire is and the standard deviation of the loss is 蟽=\(5000.The distribution of losses is strongly right-skewed: many policies have \)0loss, but a few have large losses. The company hopes to sell 1000 of these policies for \(300each.

a. Assuming that the company鈥檚 claim is true, what is the probability that the mean loss from fire is greater than \)300for an SRS of 1000 homeowners?

b. If the company wants to be 90% certain that the mean loss from fire in an SRS of 1000 homeowners is less than the amount it charges for the policy, how much should the company charge?

The probability distribution for the number of heads in four tosses of a coin is given by

Number of heads
01234
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0.06250.2500
0.3750
0.2500
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The probability of getting at least one tail in four tosses of a coin is

a. 0.2500

b. 0.3125

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d. 0.9375

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Social scientists are interested in the association between high school graduation rate (HSGR, measured as a percent) and the percent of U.S. families living in poverty (POV). Data were collected from all 50 states and the District of Columbia, and a regression analysis was conducted.

The resulting least-squares regression line is given by POV鈭�=59.2-0.620(HSGR) POV^=59.2-0.620(HSGR) with r2=0.802r2=0.802. Based on the information, which of the following is the best interpretation for the slope of the least-squares regression line?

a. For each 1% increase in the graduation rate, the percent of families living in poverty is predicted to decrease by approximately 0.896 .

b. For each 1 % increase in the graduation rate, the percent of families living in poverty is predicted to decrease by approximately 0.802.

c. For each 1 % increase in the graduation rate, the percent of families living in poverty is predicted to decrease by approximately 0.620.

d. For each 1 % increase in the percent of families living in poverty, the graduation rate is predicted to decrease by approximately 0.802.

e. For each 1 % increase in the percent of families living in poverty, the graduation rate is predicted to decrease by approximately 0.620.

More homework Some skeptical Ap庐 Statistics students want to investigate the newspaper's claim in Exercise 11, so they choose an SRS of 100students from the school to interview. In their sample, 45students completed their homework last week. Does this provide convincing evidence that less than 60%of all students at the school completed their assigned homework last week?

a. What is the evidence that less than 60%of all students completed their assigned homework last week?

b. Provide two explanations for the evidence described in part (a).

We used technology to simulate choosing 250SRSs of size n=100n=100from a population of 2000students where 60%completed their assigned homework last week. The dotplot shows pp^the sample proportion of students who completed their assigned homework last week for each of the 250simulated samples.

c. There is one dot on the graph at 0.73. Explain what this value represents.

d. Would it be surprising to get a sample proportion of p=0.45p^=0.45or smaller in an SRS of size 100when p=0.60p=0.60? Justify your answer.

e. Based on your previous answers, is there convincing evidence that less than 60%of all students at the school completed their assigned homework last week? Explain your reasoning.

Making auto parts A grinding machine in an auto parts plant prepares axles with a target diameter 渭=40.125millimeters (mm). The machine has some variability, so the standard deviation of the diameters is 蟽=0.002mm. The machine operator inspects a random sample of 4 axles each hour for quality control purposes and records the sample mean diameter x-x炉. Assume the machine is working properly.

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b. Calculate and interpret the standard deviation of the sampling distribution of x-x炉.
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