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The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset Vaia Explanations$ Math

6th Edition · 837 pages

ISBN: 9781319113339

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

Marcella takes a shower every morning when she gets up. Her time in the shower varies according to a Normal distribution with mean $4.5$ minutes and standard deviation $0.9$ minutes.

a. Find the probability that Marcella’s shower lasts between $3$ and $6$ minutes on a randomly selected day.

b. If Marcella took a $7$ minute shower, would it be classified as an outlier by the $1.5 I Q R$ rule? Justify your answer.

c. Suppose we choose $10$ days at random and record the length of Marcella’s shower each day. What’s the probability that her shower time is $7$ minutes or greater on at least $2$ of the days?

d. Find the probability that the mean length of her shower times on these 10 days exceeds $5$ minutes.

R12.5 Light intensity In a physics class, the intensity of a 100-watt light bulb was measured by a sensor at various distances from the light source. Here is a scatterplot of the data. Note that a candela is a unit of luminous intensity in the International System of Units.

Physics textbooks suggest that the relationship between light intensity y and distance x should follow an “inverse square law,” that is, a power law model of the form $y = a x^{- 2} = a \frac{1}{x^{2}}$ . We transformed the distance measurements by squaring them and then taking their reciprocals. Here is some computer output and a residual plot from a least-squares regression analysis of the transformed data. Note that the horizontal axis on the residual plot displays predicted light intensity.

a. Did this transformation achieve linearity? Give appropriate evidence to justify your answer.
b. What is the equation of the least-squares regression line? Define any variables you use.
c. Predict the intensity of a 100-watt bulb at a distance of 2.1 meters.

Exercises T12.4–T12.8 refer to the following setting. An old saying in golf is “You drive for show and you putt for dough.” The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69 of the nearly 1000 players on the PGA Tour’s world money list are examined. The average number of putts per hole (fewer is better) and the player’s total winnings for the previous season are recorded and a least-squares regression line was fitted to the data. Assume the conditions for
inference about the slope are met. Here is computer output from the regression analysis:

T12.5 Suppose that the researchers test the hypotheses $H 0 : β_{1} = 0$ versus

$H a : β_{1} < 0$ . Which of the following is the value of the t statistic for this

a. 2.61

b. −2.44

c. 2.44

d. −20.24

e. 0.081

Exercises T12.4–T12.8 refer to the following setting. An old saying in golf is “You drive for show and you putt for dough.” The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69 of the nearly 1000 players on the PGA Tour’s world money list are examined. The average number of putts per hole (fewer is better) and the player’s total winnings for the previous season are recorded and a least-squares regression line was fitted to the data. Assume the conditions for
inference about the slope are met. Here is computer output from the regression analysis:

T12.6 The P -value for the test in Exercise T12.5 is 0.0087. Which of the following is a correct interpretation of this result?
a. The probability there is no linear relationship between average number of putts per hole and total winnings for these 69 players is 0.0087.
b. The probability there is no linear relationship between average number of putts per hole and total winnings for all players on the PGA Tour’s world money list is 0.0087.
c. If there is no linear relationship between average number of putts per hole and total winnings for the players in the sample, the probability of getting a random sample of 69 players that yields a least-squares regression line with a slope of −4,139,198 or less is 0.0087.
d. If there is no linear relationship between average number of putts per hole and total winnings for the players on the PGA Tour’s world money list, the probability of getting a random sample of 69 players that yields a least-squares regression line with a slope of −4,139,198 or less is 0.0087.
e. The probability of making a Type I error is 0.0087.

Exercises T12.4–T12.8 refer to the following setting. An old saying in golf is “You drive for show and you putt for dough.” The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69 of the nearly 1000 players on the PGA Tour’s world money list are examined. The average number of putts per hole (fewer is better) and the player’s total winnings for the previous season are recorded and a least-squares regression line was fitted to the data. Assume the conditions for inference about the slope are met. Here is computer output from the regression analysis:

T12.7 Which of the following is the 95% confidence interval for the slope β1 of the population regression line?
a. $7, 897, 179 \pm 3, 023, 782$
b. $7, 897, 179 \pm 2.000 (3, 023, 782$ )
c. $- 4, 139, 198 \pm 1, 698, 371$
d. $- 4, 139, 198 \pm 1.960 (1, 698, 371)$
e. $- 4, 139, 198 \pm 2.000 (1, 698, 371)$

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