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Chapter 12: Q. AP4.31 (page 832)

AP4.31 A city wants to conduct a poll of taxpayers to determine the level of support for constructing a new city-owned baseball stadium. Which of the following is the main reason for using a large sample size in constructing a confidence interval to estimate the proportion of city taxpayers who would support such a project?
a.To increase the confidence level
b. To eliminate any confounding variables
c.To reduce nonresponse bias
d. To increase the precision of the estimate
e. To reduce undercoverage

Short Answer

Expert verified

The correct answer is option (d) To increase the precision of the estimate.

Step by step solution

01

Given information

To determine the main reason for using a large sample size in constructing a confidence interval to estimate the proportion of city taxpayers who would support such a project.

02

Explanation

Any experimental data that is used to establish inferences about a population from a sample must take the sample size into account. The major point for selecting a large sample size for generating a confidence interval to estimate the proportion of city taxpayers who would support such a project is because the greater the sample size, the better the estimations will be, and thus the precision of the estimate will be increased.
As a result, option (d), which increases the precision of the estimate, is the proper choice.

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Most popular questions from this chapter

A study of road rage asked random samples of 596men and 523women about their behavior while driving. Based on their answers, each respondent was assigned a road rage score on a scale of 0-20. The respondents were chosen by random-digit dialing of telephone numbers. Are the conditions for inference about a difference in means satisfied?

a. Maybe; the data came from independent random samples, but we should examine the data to check for Normality.

b. No; road rage scores on a scale of 0-20can’t be Normal.

c. No; a paired t-test should be used in this case.

d. Yes; the large sample sizes guarantee that the corresponding population distributions will be Normal.

e. Yes; we have two independent random samples and large sample sizes, and the10% condition is met.

The swinging pendulum Refer to Exercise 33. Here is a graph of the period versus length, along with output from a linear regression analysis using these variables.

a. Give the equation of the least-squares regression line. Define any variables you use. b. Use the model from part (a) to predict the period of a pendulum with length 80centimeters.

Boyle’s law Refers to Exercise 34. We took the logarithm (base 10) of the values for both volume and pressure. Here is some computer output from a linear regression analysis of the transformed data.


a. Based on the output, explain why it would be reasonable to use a power model to describe the relationship between pressure and volume.

b. Give the equation of the least-squares regression line. Be sure to define any variables you use.

c. Use the model from part (b) to predict the pressure in the syringe when the volume is 17cubic centimeters.

Braking distance, again How is the braking distance for a car related to the amount of tread left on the tires? Here are the braking distances (measured in car lengths) for a car making a panic stop in standing water, along with the tread depth of the tires (in 1/32inch):

Tread depth (1/32 inch)Breaking distance (car lengths)119.7109.8910.1810.4710.8611.2511.8412.4313.6115.2

a. Transform both variables using logarithms. Then calculate and state the least-squares regression line using the transformed variables.

b. Use the model from part (a) to calculate and interpret the residual for the trial when the tread depth was 3/32 inch.
Can physical activity in youth lead to mental sharpness in old age? A 2010study investigating this question involved9344randomly selected, mostly white women over age 65from four U.S. states. These women were asked about their levels of physical activity during their teenage years, 30s,50 s, and later years. Those who reported being physically active as teens enjoyed the lowest level of cognitive decline-only 8.5% had cognitive impairment-compared with 16.7% of women who reported not being physically active at that time.
(a) State an appropriate pair of hypotheses that the researchers could use to test whether the proportion of women who suffered a cognitive decline was significantly smaller for women who were physically active in their youth than for women who were not physically active at that time. Be sure to define any parameters you use.
(b) Assuming the conditions for performing inference are met, what inference method would you use to test the hypotheses you identified in part (a)? Do not carry out the test.
(c) Suppose the test in part (b) shows that the proportion of women who suffered a cognitive decline was significantly smaller for women who were physically active in their youth than for women who were not physically active at that time. Can we generalize the results of this study to all women aged65 and older? Justify your answer.
(d) We cannot conclude that being physically active as a teen causes a lower level of cognitive decline for women over 65, due to possible confounding with other variables. Explain the concept of confounding and give an example of a potential confounding variable in this study.
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