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Chapter 12: Q. 10 (page 797)

We record data on the population of a particular country from 1960to 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) =-13.5+0.01(years).

Based on this equation, the population of the country in the year 2020 should be about

(a)6.7

(b) 812

(c) 5,000,000

(d) 6,700,000

(e) 8,120,000.

Short Answer

Expert verified

The population of the country in the 2020 should be about5,000,000. The correct option is (c).

Step by step solution

01

Given Information

The population of the country in the year 2020 should be about log (population)=-13.5+0.01.

02

Explanation

Putting the year with 2020 :

log (population) =-13.5+0.01(2020)

=6.7

Taking the exponential

Population =106.7

Evaluate =5011872

=5000000

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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 ∑xiis exactly 10.

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

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

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

In the casting of metal parts, molten metal flows through a “gate” into a die that shapes the part. The gate velocity (the speed at which metal is forced through the gate) plays a critical role in die casting. A firm that casts cylindrical aluminum pistons examined a random sample of 12 pistons formed from the same alloy of metal. What is the relationship between the cylinder wall thickness (inches) and the gate velocity (feet per second) chosen by the skilled workers who do the casting? If there is a clear pattern, it can be used to direct new workers or to automate the process.

Construct and interpret a 95%confidence interval for the slope of the population regression line. Explain how this interval is consistent with the results of Exercise R12.2.

An old saying in golf is “You drive for show and you putt for dough.” 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 69of the nearly 1000players on the PGA Tour’s world money list are examined. The average number of putts per hole and the player’s total winnings for the previous season is recorded. A least-squares regression line was fitted to the data. The following results were obtained from statistical software.

Suppose that the researchers test the hypotheses H0:β=0: Ha:β<0. The value of the t statistic for this test is

(a)2.61

(b)2.44

(c)0.081

(d)-2.44

(e) -20.24

The P-value for the test in Question 5 is 0.0087. A correct interpretation of this result is that

(a) the probability that there is no linear relationship between an average number of putts per hole and total winnings for these 69players is 0.0087.

(b) the probability that there is no linear relationship between the average number of putts per hole and total winnings for all players on the PGA Tour’s world money list is 0.0087.

(c) if there is no linear relationship between an average number of putts per hole and total winnings for the players in the sample, the probability of getting a random sample of 69players yields a least-squares regression line with a slope of -4139198or less is 0.0087.

(d) if there is no linear relationship between an average number of putts per hole and total winnings for the players on the PGA Tour’s world money list, the probability of getting a random sample of 69 players yields a least-squares regression line with a slope of -4139198or less is 0.0087.

(e) the probability of making a Type II error is0.0087.

The slope β of the population regression line describes

(a) the exact increase in the selling price of an individual unit when its appraised value increases by \(1000

(b) the average increase in the appraised value in a population of units when the selling price increases by \)51000.

(c) the average increase in selling price in a population of units when the appraised value increases by \( 1000.

(d) the average selling price in a population of units when a unit's appraised value is 0.

(e) the average increase in appraised value in a sample of 16 units when the selling price increases by \) 1000.
See all solutions

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