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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 尾1?

a.3.0867卤0.4117

b. 3.0867卤0.8518

c.3.0867卤0.8069

d.3.0867卤0.8497

e.localid="1654193042763" 3.0867卤0.8481

Short Answer

Expert verified

The correct option is option (b)

3.0867卤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卤t*脳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卤t*SEb=3.0867卤2.069脳0.4117=3.0867卤0.8518

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Most popular questions from this chapter

A study of road rage asked random samples of 596men and 523women about their behavior while driving. Based on their answers, each respondent was assigned a road rage score on a scale of 0-20. The respondents were chosen by random-digit dialing of telephone numbers. Are the conditions for inference about a difference in means satisfied?

a. Maybe; the data came from independent random samples, but we should examine the data to check for Normality.

b. No; road rage scores on a scale of 0-20can鈥檛 be Normal.

c. No; a paired t-test should be used in this case.

d. Yes; the large sample sizes guarantee that the corresponding population distributions will be Normal.

e. Yes; we have two independent random samples and large sample sizes, and the10% condition is met.

Boyle鈥檚 law Refers to Exercise 34. We took the logarithm (base 10) of the values for both volume and pressure. 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 pressure and volume.

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 pressure in the syringe when the volume is 17cubic centimeters.

Sam has determined that the weights of unpeeled bananas from his local store have a mean of116grams with a standard deviation of 9grams. Assuming that the distribution of weight is approximately Normal, to the nearest gram, the heaviest 30%of these bananas weigh at least how much?

a.107g

b.121g

C.111g

d.125g

e.116g

The swinging pendulum Refer to Exercise 33. Here is a graph of the period versus 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 80centimeters.

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 渭y=105+4.2xwith 蟽=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.
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