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Chapter 12: Q. 14 (page 790)

The students in Mr. Shenk鈥檚 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'脳SEb=0.84042-1.746脳0.08091=0.69915114
role="math" localid="1654161040846" b+t'脳SEb=0.84042+1.746脳0.08091=0.98168886

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Most popular questions from this chapter

A Harris poll found that 54%of American adults don鈥檛 think that human beings developed from earlier species. The poll鈥檚 margin of error for 95%confidence was 3%. This means that

a. there is a 95%chance the interval (51%,57%) contains the true per cent of American adults who do not think that human beings developed from earlier species.

b. the poll used a method that provides an estimate within 3% of the truth about the population in 95%of samples.

c. if Harris conducts another poll using the same method, the results of the second poll will lie between 51%and 57%

d. there is a 3% chance that the interval is incorrect.

e. the poll used a method that would result in an interval that contains 54%in95% of all possible samples of the same size from this population.

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鈥檚 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鈥檚 shower each day. What鈥檚 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.

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=footlengthand 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:

Is there convincing evidence that height increases as footlength increases? to answer this question, test the hypothesis

a.H0:尾1=0H0:尾1=0versusH伪:尾1>0.H伪:尾1>0

b.H0:尾1=0H0:尾1=0versusH伪:尾1<H伪:尾1&lt;0

cH0:尾1=0H0:尾1=0versusH伪:尾1鈮�0.H伪:尾1鈮�0

dH0:尾1&gt;0H0:尾1>0versusH伪:尾1=0.H伪:尾1=0

e.H0:尾1=0H0:尾1=0versusH伪:尾1&gt;1.H伪:尾1>1

Pencils and GPA Is there a relationship between a student鈥檚 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.

The swinging pendulum Mrs. Hanrahan's precalculus class collected data on the length (in centimeters) of a pendulum and the time (in seconds) the pendulum took to complete one back-and-forth swing (called it's period). The theoretical relationship between a pendulum's length and its period is

period=2蟺glength

where gis a constant representing the acceleration due to gravity (in this case, g=980cm/s2g=980cm/s2). Here is a graph of the period versus length, length, along with output from a linear regression analysis using these variables.

a. Give the equation of the least-squares regression line. Define any variables you use.

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