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Chapter 7: Q. 30 (page 457)

The math department at a small school has 5teachers. The ages of these teachers are 23,34,37,42,58. Suppose you select a random sample of 4teachers and calculate the sample minimum age. Which of the following shows the sampling distribution of the sample minimum age?

a.

b.

c.

d.

e. None of these

Short Answer

Expert verified

The correct option (c) i.e.

Step by step solution

01

Given information

We need to find the correct option showing the sampling distribution of the sample minimum age.

02

Explanation

We know that

The smallest age out of the four ages in the sample are

Sample of size fourSample minimum
23,34,37,42
23
23,34,37,58
23
23,34,42,58
23
23,37,42,58
23
34,37,42,58
34

We then remark that the sample minimum sampling distribution should include 4dots at 23and 1dot at 34. (since there are 4samples with sample minimum 23and one sample with sample minimum 34).

Therefore, the correct option is (c) i.e.

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Most popular questions from this chapter

A researcher initially plans to take an SRS of size 160 from a certain population and calculate the sample mean x-x炉. Later, the researcher decides to increase the sample size so that the standard deviation of the sampling distribution of x-x炉will be half as big as when using a sample size of 160 . What sample size should the researcher use?

a. 40

b. 80

c. 320

d. 640

e. There is not enough information to determine the sample size.

Sample proportions List all 6possible SRSS of size n=2, calculate the proportion of red cars in the sample, and display the sampling distribution of the sample proportion on a dotplot. Is the sample proportion an unbiased estimator of the population proportion? Explain your answer.

COLORAGE
RED1
WHITE5
SILVER8
RED20

The Gallup Poll has decided to increase the size of its random sample of voters from about 1500 people to about 4000 people right before an election. The poll is designed to estimate the proportion of voters who favor a new law banning smoking in public buildings. The effect of this increase is to

a. reduce the bias of the estimate.

b. increase the bias of the estimate.

c. reduce the variability of the estimate.

d. increase the variability of the estimate.

e. reduce the bias and variability of the estimate.

David鈥檚 iPod has about 10,000songs. The distribution of the play times for these songs is heavily skewed to the right with a mean of 225seconds and a standard deviation of 60seconds.

a. Describe the shape of the sampling distribution of xfor SRSs of size n=5from the population of songs on David鈥檚 iPod. Justify your answer.

b. Describe the shape of the sampling distribution of x for SRSs of size n=100 from the population of songs on David鈥檚 iPod. Justify your answer.

The central limit theorem is important in statistics because it allows us to use a Normal distribution to find probabilities involving the sample mean if the

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

b. population is Normally distributed (for any sample size).

c. population is Normally distributed and the sample size is reasonably large.

d. population is Normally distributed and the population standard deviation is known (for any sample size).

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