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Chapter 7: Q. 22 (page 456)

More sample minimums List all 4possible SRSs of size n=3, calculate the minimum age for each sample, and display the sampling distribution of the sample minimum on a dot plot with the same scale as the dot plot in Exercise 20. How does the variability of this sampling distribution compare with the variability of the sampling distribution from Exercise 20? What does this indicate about increasing the sample size?

From exercise20:

Car NumberColorAge
1
Red1
2
White5
3
Silver8
4
Red20

Short Answer

Expert verified

Dot plots with sample sizes of n=3have less variability than dot plots with sample sizes of n=.

As the sample size grows, the sampling variability reduces.

Dot plot:

Step by step solution

01

Given Information

We are given following data:

Car NumberColorAge
1
Red1
2
White5
3
Silver8
4
Red20

We need to calculate the minimum age for each sample, and draw it's dot plots.

We need to explain how variability of this sampling distribution compare with the variability of the sampling distribution from Exercise20

02

Explanation

All possible samples of size 3then contain any three cars all different of population of 4cars.

Sample of size 3
1,2,3
1,3,4
1,2,4
2,3,4

The smallest age of three cars is used as a sample minimum

Sample of size 3Sample minimum
1,2,3
min(1,5,8) = 1
1,2,4
min(1,5,20) = 1
1,3,4
min(1,8,20) = 1
2,3,4
min(5,8,20) = 5

From above data our Dot plot will be:

In exercise 20dot plots varies in range of 1to 8, whereas in this problem dot plot ranges from 1to 5

As a result, dot plots with sample sizes of n=3have less variability than dot plots with sample sizes of n=2.

This also means that as the sample size grows, the sampling variability reduces.

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Most popular questions from this chapter

You work for an advertising agency that is preparing a new television commercial to appeal to women. You have been asked to design an experiment to compare the effectiveness of three versions of the commercial. Each subject will be shown one of the three versions and then asked to reveal her attitude toward the product. You think there may be large differences in the responses of women who are employed and those who are not. Because of these differences, you should use

a. a block design, but not a matched pairs design.

b. a completely randomized design.

c. a matched pairs design.

d. a simple random sample.

e. a stratified random sample.

Here are histograms of the values taken by three sample statistics in several hundred samples from the same population. The true value of the population parameter is marked with an arrow on each histogram.

Which statistic would provide the best estimate of the parameter? Justify your answer

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,\(25) or the statement "This ticket is not a winner." Monetary prizes can be redeemed for groceries at the store. Here is the probability distribution of the amount won on a randomly selected ticket:

Which of the following are the mean and standard deviation, respectively, of the winnings?

a. \)15.00,\(2900.00

b. \)15.00,\(53.85

c. \)15.00,\(26.93

d. \)156.25,\(53.85

e. \)156.25,$26.93

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.

Do you jog? The Gallup Poll asked a random sample of 1540 adults, "Do you happen to jog?" Suppose that the true proportion of all adults who jog is p=0.15. p=0.15.

a. What is the mean of the sampling distribution of p鈭�p^?

b. Calculate and interpret the standard deviation of the sampling distribution of p鈭�p^. Check that the 10%condition is met.

c. Is the sampling distribution of p鈭�p^approximately Normal? Justify your answer.

d. Find the probability that between 13%and17%of people jog in a random sample of 1540 adults.
See all solutions

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