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Chapter 12: Q. 20 (page 792)

Pencils and GPA Is there a relationship between a student’s GPA and the number of pencils in his or her backpack? Jordynn and Angie decided to find out by selecting a random sample of students from their high school. Here is computer output from a least-squares regression analysis using x=number of pencils and y=GPA:

Is there convincing evidence of a linear relationship between GPA and number of pencils for students at this high school? Assume the conditions for inference are met.

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Most popular questions from this chapter

Could mud wrestling be the cause of a rash contracted by University of Washington students? Two physicians at the university’s student health center wondered about this when one male and six female students complained of rashes after participating in a mud-wrestling event. Questionnaires were sent to a random sample of students who participated in the event. The results, by gender, are summarized in the following table.

Here is some computer output for the preceding table. The output includes the observed counts, the expected counts, and the chi-square statistic.

From the chi-square test performed in this study, we may conclude that

a. there is convincing evidence of an association between the gender of an individual participating in the event and the development of a rash.

b. mud wrestling causes a rash, especially for women.

c. there is absolutely no evidence of any relationship between the gender of an individual participating in the event and the subsequent development of a rash.

d. development of a rash is a real possibility if you participate in mud wrestling, especially if you do so regularly.

e. the gender of the individual participating in the event and the development of a rash are independent.

Sam has determined that the weights of unpeeled bananas from his local store have a mean of116grams with a standard deviation of 9grams. Assuming that the distribution of weight is approximately Normal, to the nearest gram, the heaviest 30%of these bananas weigh at least how much?

a.107g

b.121g

C.111g

d.125g

e.116g

Killing bacteria Expose marine bacteria to X-rays for time periods from 1to 15minutes. Here is a scatterplot showing the number of surviving bacteria (in hundreds) on a culture plate after each exposure time:


a. Below is a scatterplot of the natural logarithm of the number of surviving bacteria versus time. Based on this graph, explain why it would be reasonable to use an exponential model to describe the relationship between the count of bacteria and the time.


b). Here is the output from a linear regression analysis of the transformed data. Give the equation of the least-squares regression line. Be sure to defne any variables you use.

c. Use your model to predict the number of surviving bacteria after 17minutes.

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.

Stats teachers’ cars A random sample of 21 AP® Statistics teachers was asked to report the age (in years) and mileage of their primary vehicles. Here is a scatterplot of the data:

Here is some computer output from a least-squares regression analysis of these data. Assume that the conditions for regression inference are met.

a. Verify that the 95%confidence interval for the slope of the population regression line is (9016.4,14,244.8).

b. A national automotive group claims that the typical driver puts 15,000miles per year on his or her main vehicle. We want to test whether AP® Statistics teachers are typical drivers. Explain why an appropriate pair of hypotheses for this test is role="math" localid="1654244859513" H0:β1=15,000versus Ha:β1≠15,000.

c. Compute the standardized test statistic and P -value for the test in part (b). What conclusion would you draw at the α=0.05significance level?

d. Does the confidence interval in part (a) lead to the same conclusion as the test in part (c)? Explain your answer.
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