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Chapter 10: Q 36. (page 644)

Drive my car

a. Explain what the value of r2tells you about how well the least-squares line

fits the data.

b. The mean age of the students’ cars in the sample was x̄=5 years.

Find the mean mileage of the cars in the sample.

c. Interpret the value of s.

d. Would it be reasonable to use the least-squares line to predict a car’s mileage from its age for a Council High School teacher? Justify your answer.

Short Answer

Expert verified

a. It tells us about the variation between variables is best explained by least square regression line.

b. Mean mileage is 105800miles.

c. s=22723

d. We can't use least squares line to predict the mileage of cars of teachers.

Step by step solution

01

Given Information

It is given that

02

Importance of r2

From table, r2=77%=0.77

Hence, 77%of variation between variables is explained by least square regression line.

03

Mean Mileage

Lest square regression line is y^=a+bx

From table a=-13832

b=14954

Least square equation becomes

y^=-13832+14954x

Now, (x¯,y¯)lies on least square regression line, so mean mileage is obtained by replacing xby x¯

hence, y¯=y^

=-13832+14954x¯

=-13832+14954(8)

=105800

hence, mean mileage is105800miles.

04

Value of s

From table, s=22723

Hence, error made when predicting the mileage using least square regression line is on average22723miles.

05

Reason to use Least Square Line

It is due to the fact that least square was determined using data of students.

It is not representative of teachers and we cannot it to predict the mileage of cars of teachers.

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Most popular questions from this chapter

At a baseball game, 42of 65randomly selected people own an iPod. At a rock concert occurring at the same time across town, 34of 52randomly selected people own an iPod. A researcher wants to test the claim that the proportion of iPod owners at the two venues is different. A 90%confidence interval for the difference (Game − Concert) in population proportions is (−0.154,0.138). Which of the following gives the correct outcome of the researcher’s test of the claim?

a. Because the confidence interval includes 0, the researcher can conclude that the proportion of iPod owners at the two venues is the same.

b. Because the center of the interval is -0.008, the researcher can conclude that a higher proportion of people at the rock concert own iPods than at the baseball game.

c. Because the confidence interval includes 0, the researcher cannot conclude that the proportion of iPod owners at the two venues is different.

d. Because the confidence interval includes more negative than positive values, the researcher can conclude that a higher proportion of people at the rock concert own iPods than at the baseball game.

e. The researcher cannot draw a conclusion about a claim without performing a significance test.

TicksLyme disease is spread in the northeastern United States by infected ticks. The ticks are infected mainly by feeding on mice, so more mice result in more infected ticks. The mouse population, in turn, rises and falls with the abundance of acorns, their favored food. Experimenters studied two similar forest areas in a year when the acorn crop failed. To see if mice are more likely to breed when there are more acorns, the researchers added hundreds of thousands of acorns to one area to imitate an abundant acorn crop, while leaving the other area untouched. The next spring, 54of the 72mice trapped in the first area were in breeding condition, versus 10of the 17mice trapped in the second area.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameters of interest.

b. Check if the conditions for performing the test are met.

A random sample of size nwill be selected from a population, and the proportion of those in the sample who have a Facebook page will be calculated. How would the margin of error for a 95%confidence interval be affected if the sample size were increased from 50to 200?

(a) It remains the same.

(b) It is multiplied by 2.

(c) It is multiplied by 4.

(d) It is divided by 2.

(e) It is divided by 4.

Suppose the true proportion of people who use public transportation to get to work in the Washington, D.C. area is 0.45. In a simple random sample of 250people who work in Washington, about how far do you expect the sample proportion to be from the true proportion?

a. 0.4975

b. 0.2475

c. 0.0315

d. 0.0009

e.0

Children make choices Refer to Exercise 15.

a. Explain why the sample results give some evidence for the alternative hypothesis.

b. Calculate the standardized test statistic and P-value.

c. What conclusion would you make?
See all solutions

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