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Chapter 12: Q.27 (page 793)

Multiple Choice Select the best answer for Exercises 23-28. Exercises 23-28 refer to the following setting. To see if students with longer feet tend to be taller, a random sample of 25students was selected from a large high school. For each student, x=footlength&y=heightwere recorded. We checked that the conditions for inference about the slope of the population regression line are met. Here is a portion of the computer output from a least-squares regression analysis using these data:

Which of the following is a 95%confidence interval for the population slope β1?

a.3.0867±0.4117

b. 3.0867±0.8518

c.3.0867±0.8069

d.3.0867±0.8497

e.localid="1654193042763" 3.0867±0.8481

Short Answer

Expert verified

The correct option is option (b)

3.0867±0.8518

Step by step solution

01

Given Information

Given in the question that

n=25

c=0.95

we have to determine the correct option.

02

Explanation

The confidence interval is computed as

b±t*×SEb

where b1=3.0867and SEb1=0.4117which is given in the computer output.

The degree of difference is

df=n-2=25-2=23

The critical T value can be found in the Tdistribution table, so t*is2.069.

Therefore, the confidence interval is

localid="1654497378353" b±t*SEb=3.0867±2.069×0.4117=3.0867±0.8518

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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.

The swinging pendulum Refer to Exercise 33. We took the logarithm (base 10) of the values for both length and period. Here is some computer output from a linear regression analysis of the transformed data.


a. Based on the output, explain why it would be reasonable to use a power model to describe the relationship between the length and period of a pendulum.

b. Give the equation of the least-squares regression line. Be sure to define any variables you use.

c. Use the model from part (b) to predict the period of a pendulum with a length of 80cm.

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d. P(z<0.3-0.4(0.4)(0.6)60)Pz&lt;0.3-0.4(0.4)(0.6)60

c. P(z<0.3-0.4(0.4)(0.6)60)

Pz&lt;0.3-0.4(0.4)(0.6)60

e. P(z<0.4-0.3(0.3)(0.7)60)Pz&lt;0.4-0.3(0.3)(0.7)60

Pricey diamonds Here is a scatterplot showing the relationship between the
weight (in carats) and price (in dollars) of round, clear, internally flawless diamonds with excellent cuts:

a. Explain why a linear model is not appropriate for describing the relationship between price and weight of diamonds.
b. We used software to transform the data in hopes of achieving linearity. The output shows the results of two different transformations. Would an exponential model or a power model describe the relationship better? Justify your answer.

c. Use each model to predict the price for a diamond of this type that weighs 2 carats. Which prediction do you think will be better? Explain your reasoning.

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.

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d. The range of age is greater for Team A

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