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Chapter 10: Q. T10.9 (page 699)

Are TV commercials louder than their surrounding programs? To find out, researchers collected data on 50randomly selected commercials in a given week. With the television’s volume at a fixed setting, they measured the maximum loudness of each commercial and the maximum loudness in the first 30seconds of regular programming that followed. Assuming conditions for inference are met, the most appropriate method for answering the question of interest is

a. a two-sample t test for a difference in means.

b. a two-sample t interval for a difference in means.

c. a paired t test for a mean difference.

d. a paired t interval for a mean difference.

e. a two-sample z test for a difference in proportions.

Short Answer

Expert verified

Option(e) A two-sample z test for a difference in proportions is the most appropriate method for this question.

Step by step solution

01

Given information

We need to find most appropriate method for answering the question.

02

Simplify

In general, we know that there is a one-sample z test for each proportion.
However, there is a two-sample z test for two proportions.
Similarly, there is one sample t test for one mean and two sample t tests or intervals or paired t tests or intervals for two means.

For checking a difference, equality, increase, or reduction, use a test.
To estimate an interval in which the true value lies, use an interval.
Therefore, a two-sample z test for a difference in proportions in this query because we need to estimate the difference between the two proportions.
As a result, option (e) is the proper choice.

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Most popular questions from this chapter

Response bias Does the appearance of the interviewer influence how people respond to a survey question? Ken (white, with blond hair) and Hassan (darker, with Middle Eastern features) conducted an experiment to address this question. They took turns (in a random order) walking up to people on the main street of a small town, identifying themselves as students from a local high school, and asking them, “Do you support President Obama’s decision to launch airstrikes in Iraq?” Of the 50people Hassan spoke to, 11said “Yes,” while 21of the 44people Ken spoke to said “Yes.” Construct and interpret a 90%confidence interval for the difference in the proportion of people like these who would say they support President Obama’s decision when asked by Hassan versus when asked by Ken.

The power takeoff driveline on tractors used in agriculture is a potentially serious hazard to operators of farm equipment. The driveline is covered by a shield in new tractors, but for a variety of reasons, the shield is often missing on older tractors. Two types of shields are the bolt-on and the flip-up. It was believed that the boll-on shield was perceived as a nuisance by the operators and deliberately removed, but the flip-up shield is easily lifted for inspection and maintenance and may be left in place. In a study initiated by the US National Safety Council, random samples of older tractors with both types of shields were taken to see what proportion of shields were removed. Of 183tractors designed to have bolt-on shields, 35had been removed. Of the 156tractors with flip-up shields, 15were removed. We wish to perform a test of H0:pb=pfversus Ha:pb>pf, where pband pfare the proportions of all the tractors with bolt-on and flip-up shields removed, respectively. Which of the following is not a condition for performing the significance test ?

(a) Both populations are Normally distributed.

(b) The data come from two independent samples.

(c) Both samples were chosen at random.

(d) The counts of successes and failures are large enough to use Normal calculations.

(e) Both populations are at least 10times the corresponding sample sizes.

A scatterplot and a least-squares regression line are shown in the figure. What effect does point P have on the slope of the regression line and the correlation?

a. Point P increases the slope and increases the correlation.

b. Point P increases the slope and decreases the correlation.

c. Point P decreases the slope and decreases the correlation.

d. Point P decreases the slope and increases the correlation .

e. No conclusion can be drawn because the other coordinates are unknown.

Digital video disks A company that records and sells rewritable DVDs wants to compare the reliability of DVD fabricating machines produced by two different manufacturers. They randomly select 500DVDs produced by each fabricator and find that 484of the disks produced by the first machine are acceptable and 480of the disks produced by the second machine are acceptable. If p1,p2are the proportions of acceptable DVDs produced by the first and second machines, respectively, check if the conditions for calculating a confidence interval for p1-p2are met.

Shortly before the 2012presidential election, a survey was taken by the school newspaper at a very large state university. Randomly selected students were asked, “Whom do you plan to vote for in the upcoming presidential election?” Here is a two-way table of the responses by political persuasion for 1850students:

Candidate of

choice


Political persuasion

Democrat
Republican
Independent
Total
Obama
925
78
26
1029
Romney
78
598
19
695
Other
2
8
11
21
Undecided
32
28
45
105
Total
1037
712
101
1850

Which of the following statements about these data is true?

a. The percent of Republicans among the respondents is 41%.

b. The marginal relative frequencies for the variable choice of candidate are given by

Obama: 55.6%; Romney: 37.6%; Other: 1.1%; Undecided: 5.7%.

c. About 11.2%of Democrats reported that they planned to vote for Romney.

d. About 44.6%of those who are undecided are Independents.

e. The distribution of political persuasion among those for whom Romney is the

candidate of choice is Democrat: 7.5%; Republican: 84.0%; Independent: 18.8%.
See all solutions

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