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Chapter 12: Q. T12.10 (page 824)

T12.10We record data on the population of a particular country from 1960 to 2010. A
scatterplot reveals a clear curved relationship between population and year. However, a different scatterplot reveals a strong linear relationship between the logarithm (base 10) of the population and the year. The least-squares regression line for the transformed data is
log(population)=^鈭�13.5+0.01(year)
Based on this equation, which of the following is the best estimate for the population of the country in the year 2020?
a. 6.7
b. 812
c. 5,000,000
d. 6,700,000
e. 8,120,000

Short Answer

Expert verified

The correct answer is option (c) 5,000,000.

Step by step solution

01

Given information

To determine the best estimate for the population of the country in the year 2020.

02

Explanation

A scatterplot shows that the population and year have a clear curving relationship. A separate scatterplot, on the other hand, displays a significant linear link between the population logarithm and the year.
The following is the linear regression line:
ln(P~opulation)=-13.5+0.01(Year)
By 2020, the year will be replaced, and it will be:
ln(P~opulation)=-13.5+0.01(Year)
鈬�ln(Population)=-13.5+0.01(2020)
=6.7
Take each side's exponential:
Population=106.7
=5011872
鈮�5000000
As a result, option (c)5000000 is the correct option.

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Most popular questions from this chapter

Exercises T12.4鈥揟12.8 refer to the following setting. An old saying in golf is 鈥淵ou drive for show and you putt for dough.鈥� The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69 of the nearly 1000 players on the PGA Tour鈥檚 world money list are examined. The average number of putts per hole (fewer is better) and the player鈥檚 total winnings for the previous season are recorded and a least-squares regression line was fitted to the data. Assume the conditions for inference about the slope are met. Here is computer output from the regression analysis:

T12.7 Which of the following is the 95% confidence interval for the slope 尾1 of the population regression line?
a. 7,897,179卤3,023,782
b. 7,897,179卤2.000(3,023,782)
c. 鈭�4,139,198卤1,698,371
d. 鈭�4,139,198卤1.960(1,698,371)
e. 鈭�4,139,198卤2.000(1,698,371)

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.

An experimenter wishes to test if one of two types of fish food (a standard fish food and a new product) is better for producing fish of equal weight after a two-month feeding program. The experimenter has two identical fish tanks (1 and 2) and is considering how to assign 40 fish, each of which has a numbered tag, to the tanks. The best way to do this would be to

a. put all the odd-numbered fish in Tank 1 and the even-numbered fish in Tank 2. Give the standard food to Tank 1 and the new product to Tank 2.

b. obtain pairs of fish whose weights are roughly equal at the start of the experiment and randomly assign one of the pair to Tank 1 and the other to Tank 2. Give the standard food to Tank 1 and the new product to Tank 2.

c. proceed as in option (b), but put the heavier of each pair into Tank 2. Give the standard food to Tank 1 and the new product to Tank 2.

d. assign the fish completely at random to the two tanks using a coin flip: heads means Tank 1 and tails means Tank 2. Give the standard food to Tank 1 and the new product to Tank 2.

e. divide the 40 fish into two groups, with the 20 heaviest fish in one group. Randomly choose which tank to assign the heaviest fish and assign the lightest fish to the other tank. Give the standard food to Tank 1 and the new product to Tank 2.

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

Section I: Multiple ChoiceChoose the best answer for Questions AP4.1鈥揂P4.40.
AP4.1 A major agricultural company is testing a new variety of wheat to determine whether it is more resistant to certain insects than the current wheat variety. The proportion of a current wheat crop lost to insects is 0.04. Thus, the company wishes to test the following hypotheses:
H0:p=0.04

Ha:p<0.04

Which of the following significance levels and sample sizes would lead to the highest power for this test?
a. n=200 and 伪=0.01
b. n=400and 伪=0.05
c.n=400and 伪=0.01
d. n=500and 伪=0.01
e. n=500 and 伪=0.05
See all solutions

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