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Chapter 12: Q. 14 (page 790)

The students in Mr. Shenk’s class measured the arm spans and heights (in inches) of a random sample of 18students from their large high school. Here is computer output from a least-squares regression analysis of these data. Construct and interpret a 90%confidence interval for the slope of the population regression line. Assume that the conditions for performing inference are met.

PredictorCoefStdevt-ratioPConstant11.5475.6002.060.056Armspan0.840420.0809110.390.000S=1.613R-Sq=87.1%R-Sq(adj)=86.3%

Short Answer

Expert verified

We are 90%confident that the slope of the true regression line is between 0.69915114and0.98168886.

Step by step solution

01

Given Information

We need to construct and interpret a 90%confidence interval for the slope of the population regression line.

02

Simplify

Consider:

n=18b=0.84042SEb=0.08091

The degrees of freedom in sample size decreased by 2:

df=n-2=18-2=16

The critical t-value can be found in table B in the row of df=16and the column of c=90%

t'=1.746

The boundaries of the confidence interval then become:

b-t'×SEb=0.84042-1.746×0.08091=0.69915114
role="math" localid="1654161040846" b+t'×SEb=0.84042+1.746×0.08091=0.98168886

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Most popular questions from this chapter

Insurance adjusters are always concerned about being overcharged for accident repairs. The adjusters suspect that Repair Shop1quotes higher estimates than Repair Shop2. To check their suspicion, the adjusters randomly select 12cars that were recently involved in an accident and then take each of the cars to both repair shops to obtain separate estimates of the cost to fix the vehicle. The estimates are given in hundreds of dollars.

Assuming that the conditions for inference are met, which of the following significance tests should be used to determine whether the adjusters’ suspicion is correct?

a. A pairedt test

b. A two-sample ttest

c. A t test to see if the slope of the population regression line is0

d. A chi-square test for homogeneity

e. A chi-square test for goodness of fit

Section I: Multiple ChoiceChoose the best answer for Questions AP4.1–AP4.40.
AP4.1 A major agricultural company is testing a new variety of wheat to determine whether it is more resistant to certain insects than the current wheat variety. The proportion of a current wheat crop lost to insects is 0.04. Thus, the company wishes to test the following hypotheses:
H0:p=0.04

Ha:p<0.04

Which of the following significance levels and sample sizes would lead to the highest power for this test?
a. n=200 and α=0.01
b. n=400and α=0.05
c.n=400and α=0.01
d. n=500and α=0.01
e. n=500 and α=0.05

Predicting height Using the health records of every student at a high school, the school nurse created a scatterplot relating y=height (in centimeters) to x=age (in years). After verifying that the conditions for the regression model were met, the nurse calculated the equation of the population regression line to be μy=105+4.2xwith σ=7cm.

a. According to the population regression line, what is the average height of 15-year-old students at this high school?

b. About what percent of 15-year-old students at this school are taller than 180cm?

c. If the nurse used a random sample of 50students from the school to calculate the regression line instead of using all the students, would the slope of the sample regression line be exactly 4.2? Explain your answer.

Marcella takes a shower every morning when she gets up. Her time in the shower varies according to a Normal distribution with mean 4.5minutes and standard deviation 0.9minutes.

a. Find the probability that Marcella’s shower lasts between 3and 6minutes on a randomly selected day.

b. If Marcella took a 7minute shower, would it be classified as an outlier by the 1.5IQRrule? Justify your answer.

c. Suppose we choose 10days at random and record the length of Marcella’s shower each day. What’s the probability that her shower time is 7minutes or greater on at least 2of the days?

d. Find the probability that the mean length of her shower times on these 10 days exceeds5 minutes.

Beer and BAC Refer to Exercise 5. Here is computer output from the least-squares regression analysis of the beer and blood alcohol data.

a. What is the estimate for β0? Interpret this value.

b. What is the estimate for β1? Interpret this value.

c. What is the estimate for σ? Interpret this value.

d. Give the standard error of the slope SEb1. Interpret this value.
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