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Chapter 7: Q. 2.8 (page 489)

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.

Short Answer

Expert verified

(a) we should use a block design, but not a matched pairs design.

Step by step solution

01

Given Information

You work for a marketing firm, and you're working on a new television commercial aimed towards women. You've been given the task of designing an experiment to compare the effectiveness of three different commercial versions. Each subject will be shown one of the three versions of the product and then asked to express her feelings about it. You believe there are significant variations in the responses of working and unemployed women.

02

Explanation for correct option

Since d and e are not designs, but rather sampling techniques, they can be deleted. Because there are only two levels of treatment, a matched pair design is utilised. Because it is not a matched pair design, answer c is not required to be considered. There are more than one element, thus the b isn't taken into account. Completely randomised design and randomised block design are the remaining options. The answer is randomised block design, because this design wishes to take that into account.

As a result, the best solution is (a)

03

Explanation for incorrect option

Option 'b' a completely randomized design is not the correct answer.

Option 'c' a matched pairs design is not the correct answer.

Option 'd' a simple random sample is not the correct answer.

Option'e' a stratified random sample is not the correct answer.

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Most popular questions from this chapter

Detecting gypsy moths The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. Each month, an SRS of 50 traps is inspected, the number of moths in each trap is recorded, and the mean number of moths is calculated. Based on years of data, the distribution of moth counts is discrete and strongly skewed with a mean of 0.5 and a standard deviation of 0.7.

a. Explain why it is reasonable to use a Normal distribution to approximate the sampling distribution of x-x炉for SRSs of size 50 .

b. Estimate the probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6.

c. In a recent month, the mean number of moths in an SRS of size 50 was x-=0.6. x炉=0.6. Based on this result, is there convincing evidence that the moth population is getting larger in this state? Explain your reasoning.

Dead battery? A car company claims that the lifetime of its batteries varies from car to car according to a Normal distribution with mean 渭=48months and standard deviation 蟽=8.2months. A consumer organization installs this type of battery in an SRS of 8 cars and calculates x炉=42.2months.

a. Find the probability that the sample mean lifetime is 42.2 months or less if the company's claim is true.

b. Based on your answer to part (a), is there convincing evidence that the company is overstating the average lifetime of its batteries?

Suppose that you are a student aide in the library and agree to be paid according to the "random pay" system. Each week, the librarian flips a coin. If the coin comes up heads, your pay for the week is 80\(. If it comes up tails, your pay for the week is 40\). You work for the library for 100 weeks. Suppose we choose an SRS of 2 weeks and calculate your average earnings x-x炉. The shape of the sampling distribution of will be

a. Normal.

b. approximately Normal.

c. right-skewed.

d. left-skewed.

e. symmetric but not Normal.

Five books An author has written 5 children's books. The numbers of pages in these books are 64,66,71,73, and 76 .

a. List all 10 possible SRSs of size n=3,n=3, calculate the median number of pages for each sample, and display the sampling distribution of the sample median on a dotplot.

b. Describe how the variability of the sampling distribution of the sample median would change if the sample size was increased to n=4.n=4.

c. Construct the sampling distribution of the sample median for samples of size n=4. n=4. Does this sampling distribution support your answer to part (b)? Explain your reasoning.

The number of hours a lightbulb burns before failing varies from bulb to bulb. The population distribution of burnout times is strongly skewed to the right. The central limit theorem says that

a. as we look at more and more bulbs, their average burnout time gets ever closer to the mean 渭 for all bulbs of this type.

b. the average burnout time of a large number of bulbs has a sampling distribution with the same shape (strongly skewed) as the population distribution.

c. the average burnout time of a large number of bulbs has a sampling distribution with a similar shape but not as extreme (skewed, but not as strongly) as the population distribution.

d. the average burnout time of a large number of bulbs has a sampling distribution that is close to Normal.

e. the average burnout time of a large number of bulbs has a sampling distribution that is exactly Normal.
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