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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

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=ax-2=a1x2. 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.

The following back-to-back stem plots compare the ages of players from two minor-league hockey teams (1/7=17 years)

Which of the following cannot be justified from the plots?

a. Team A has the same number of players in their 30sas does Team B.

b. The median age of both teams is the same.

c. Both age distributions are skewed to the right.

d. The range of age is greater for Team A

e. There are no outliers by the1.5IQR rule in either distribution.

SAT Math scores Is there a relationship between the percent of high school graduates in each state who took the SAT and the state’s mean SAT Math score? Here is a residual plot from a linear regression analysis that used data from all 50states in a recent year. Explain why the conditions for performing inference about the slope β1 of the population regression line are not met.

Determining tree biomass It is easy to measure the diameter at breast height (in centimeters) of a tree. It’s hard to measure the total aboveground biomass (in kilograms) of a tree because to do this, you must cut and weigh the tree. Biomass is important for studies of ecology, so ecologists commonly estimate it using a power model. The following figure is a scatterplot of the natural logarithm of biomass against the natural logarithm of diameter at breast height (DBH) for 378trees in tropical rain forests. The least-squares regression line for the transformed data is lny∧=-2.00+2.42lnx∧lny^=-2.00+2.42lnx^

Use this model to estimate the biomass of a tropical tree 30cm in diameter.

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.
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