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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*脳SEb=0.84042-1.746脳0.08091=0.69915114

localid="1650689713665" b+t*脳SEb=0.84042+1.746脳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

A distribution that represents the number of cars parked in a randomly selected residential driveway on any night is given by

xi:0 123 4
pi :0.10.20.350.250.15

Which of the following statements is correct?

(a) This is a legitimate probability distribution because each of the pi-values is between 0and 1.

(b) This is a legitimate probability distribution because 鈭�xiis exactly 10.

(c) This is a legitimate probability distribution because each of the pi-values is between 0and 1and the 鈭�xiis exactly 10.

(d) This is not a legitimate probability distribution because 鈭�xiis not exactly 10.

(e) This is not a legitimate probability distribution because role="math" localid="1650523963322" 鈭�pi is not exactly 1.

The cell that contributes most to the chi-square statistic is

(a) men who developed a rash.

(b) men who did not develop a rash.

(c) women who developed a rash.

(d) women who did not develop a rash.

(e) both (a) and (d).

Question refers to the following situation:

Could mud wrestling be the cause of a rash contracted by University of Washington students? Two physicians at the University of Washington 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.

Some Minitab output for the previous table is given below. The output includes the observed counts, the expected counts, and the chi-square statistic.

Students in a statistics class drew circles of varying diameters and counted how many Cheerios could be placed in the circle. The scatterplot shows the results.

The students want to determine an appropriate equation for the relationship between diameter and the number of Cheerios. The students decide to transform the data to make it appear more linear before computing a least-squares regression line. Which of the following single transformations would be reasonable for them to try?

I. Take the square root of the number of Cheerios.

II. Cube the number of Cheerios.

III. Take the log of the number of Cheerios.

IV. Take the log of the diameter.

(a) I and II

(b) I and III

(c) II and III

(d) II and IV

(e) I and IV

Could mud wrestling be the cause of a rash contracted by University of Washington students? Two physicians at the University of Washington 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.

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 development of a rash.

(b) mud wrestling causes a rash, especially for women.

(c) there is absolutely no evidence of any relation 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 on a regular basis.

(e) the gender of the individual participating in the event and the development of a rash are independent.

6. Beer and BAC Refer to Exercise 4. Computer output from the least-squares regression analysis on the beer and blood alcohol data is shown below.


The model for regression inference has three parameters:伪,尾and蟽Explain what each parameter represents in context. Then provide an estimate for each.
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