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Chapter 12: Q. 10 (page 761)

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

Short Answer

Expert verified

We are 90% confident that the slope of the true regression line is between 0.69915114 and 0.98168886.

Step by step solution

01

Given Information

Given:

n=18

SEb=0.08091

02

Explanation

The degrees of freedom is the 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 d f=16 and in the column of c=90% :

t*=1.746

The boundaries of the confidence interval then become:

localid="1650689704858" b-t*×SEb=0.84042-1.746×0.08091=0.69915114

localid="1650689713665" b+t*×SEb=0.84042+1.746×0.08091=0.98168886

We are 90% confident that the slope of the true regression line is between 0.69915114 and 0.98168886.

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Most popular questions from this chapter

Beavers and beetles Refer to Exercise 9.

(a) How many clusters of beetle larvae would you predict in a circular plot with 5 tree stumps cut by beavers? Show your work.

(b) About how far off do you expect the prediction in part (a) to be from the actual number of clusters of beetle larvae? Justify your answer.

Which of the following is not one of the conditions that must be satisfied in order to perform inference about the slope of a least-squares regression line? (a) For each value of x, the population of y-values is Normally distributed.

(b) The standard deviation σof the population of y-values corresponding to a particular value of x is always the same, regardless of the specific value of x. (c) The sample size—that is, the number of paired observations (x, y)—exceeds 30.

(d) There exists a straight line y=α+βxsuch that, for each value of x, the mean μyof the corresponding population of y-values lies on that straight line.

(e) The data come from a random sample or a randomized experiment.

A survey firm wants to ask a random sample of adults in Ohio if they support an increase in the state sales tax from 5%% to 6%, with the additional revenue going to education. Let p^denote the proportion in the sample who say that they support the increase. Suppose that 40%of all adults in Ohio support the increase. How large a sample would be needed to guarantee that the standard deviation of p^is no more than 0.01?

(a)1500

(b) 2400

(c)2401

(d) 2500

(e)9220

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Based on footprints and some other sketchy evidence, some people think that a large apelike animal, called Sasquatch or Bigfoot, lives in the Pacific Northwest. His weight is estimated to be about 280pounds, or 127kilograms. How big is Bigfoot’s brain? Show your method clearly

Time at the table Refer to Exercise 14.

(a) Construct and interpret a 98% confidence interval for the slope of the population regression line. Explain how your results are consistent with the significance test in Exercise 14.

(b) Interpret each of the following in context:

(i)s

(ii) r2

(iii) The standard error of the slope
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