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Chapter 10: Q.4 (page 662)

Men versus women The National Assessment of Educational Progress (NAEP) Young Adult Literacy Assessment Survey interviewed a random sample of 1917people 21to 25years old. The sample contained 840men and 1077women. 49The mean and standard deviation of scores on the NAEP's test of quantitative skills were x¯1=272.40and s1=59.2for the men in the sample. For the women, the results were x¯2=274.73and s2=57.5. Is the difference between the mean scores for men and women significant at the 1% level? Give appropriate statistical evidence to justify your answer.

Short Answer

Expert verified

No, there is not enough proof to help the claim that there is a difference.

Step by step solution

01

Given Information

x¯1=272.40

x¯2=274.73

s1=59.2

s2=57.5

n1=840

n2=1077

02

Explanation

The hypothesis

H0:μ1=μ2

H1:μ1≠μ2

The test statistic:

t=x¯1-x¯2s12n1+s22n1

=272.40-274.7259.22840+57.521077

=-0.866

03

Explanation

The degrees of freedom:

df=minn1-1,n2-1

=min(840-1,1077-1)

=839>100

The P-value is the probability of obtaining the value of the test statistic, or a value more extreme.

localid="1650369677218" 0.30=2×0.15<P<2×0.20

=0.40

localid="1650352701568" 0.30<P<0.40

The P-value is the chance of getting the test statistic's result, or a number that is more severe.

P>0.01=1%⇒Fail to rejectH0

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Most popular questions from this chapter

Mrs. Woods and Mrs. Bryan are avid vegetable gardeners. They use different fertilizers, and each claims that hers is the best fertilizer to use when growing tomatoes. Both agree to do a study using the weight of their tomatoes as the response variable. They had each planted the same varieties of tomatoes on the same day and fertilized the plants on the same schedule throughout the growing season. At harvest time, they each randomly select 15tomatoes from their respective gardens and weigh them. After performing a two-sample t-test on the difference in mean weights of tomatoes, they get t=5.24and P=0.0008. Can the gardener with the larger mean claim that her fertilizer caused her tomatoes to be heavier?

(a) No, because the soil conditions in the two gardens is a potential confounding variable.

(b) No, because there was no replication.

(c) Yes, because a different fertilizer was used on each garden.

(d) Yes, because random samples were taken from each garden.

Based on your answer to Question 1.3, would you be surprised if the difference in the mean amount of liquid dispensed in the two samples was12ounces? Explain

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(a) Let M =the height of a randomly selected young man and W =the height of a randomly selected young woman. Describe the shape, center, and spread of the distribution of M-W

(b) Find the probability that a randomly selected young man is at least 2inches taller than a randomly selected young woman. Show your work.

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(a) H0:μ=7.9andHa:μ<7.9

(b) H0:μ=7.9andHa:μ≠7.9

(c) H0:μ=9andHa:μ≠9

(d)H0:μ=9andHa:μ<9

(e)H0:μ≤9andHa:μ≥9

Seat belt use: The proportion of drivers who use seat belts depends on things like age (young people are more likely to go unbelted) and gender (women are more likely to use belts). It also depends on local law. In New York City, police can stop a driver who is not belted. In Boston at the time of the study, police could cite a driver for not wearing a seat belt only if the driver had been stopped for some other violation. Here are data from observing random samples of female Hispanic drivers in these two cities:

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(c) Based on the laws in the two cities, we would expect a smaller proportion of drivers to wear seat belts in Boston than in New York. Does the confidence interval in part (b) give good evidence that this is true for female Hispanic drivers? Justify your answer.
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