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Chapter 10: Q. 12 (page 668)

The correlation between the heights of fathers and the heights of their (grownup) sons isr=0.52 , both measured in inches. If fathers鈥� heights were measured in feet and sons鈥� heights were measured in furlongs (one furlong equals 7920 inches), the correlation between heights of fathers and heights of sons would be

(a) much smaller than 0.52.

(b) slightly smaller than 0.52.

(c) unchanged; equal to 0.52.

(d) slightly larger than 0.52.

(e) much larger than 0.52.

Short Answer

Expert verified

The answer is an option (c) unchanged; equal to 0.52

Step by step solution

01

Given Information

The correlation between the heights of fathers and the heights of their (grownup) sons is r=0.52, both measured in inches.

And, one furlong equals 7920 inches.

02

Explanation. 

The advantage of correlation is it's a unitless measure. If changing one of the unit measures (from feet to furlongs) resulted in a correlation change, then the value would be arbitrary since we have arbitrarily defined the units. Then, the correlation would never have any practical meaning.

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Most popular questions from this chapter

A large toy company introduces a lot of new toys to its product line each year. The company wants to predict the demand as measured by y, first-year sales (in millions of dollars) using x, awareness of the product (as measured by the proportion of customers who had heard of the product by the end of the second month after its introduction). A random sample of 65new products was taken, and a correlation of 0.96was computed. Which of the following is a correct interpretation of this value?

(a) Ninety-six percent of the time, the least-squares regression line accurately predicts first-year sales.

(b) About 92%of the time, the proportion of people who have heard of the product by the end of the second month will correctly predict first-year sales.

(c) About 92%of first-year sales can be explained by the proportion of people who have heard of the product by the end of the second month.

(d) The least-squares regression line relating the proportion of people who have heard of the product by the end of the second month and first-year sales will have a slope of 0.96.

(e) Ninety-two percent of the variation in first-year sales can be explained by the least-squares regression line with proportion of people who have heard of the product by the end of the second month as the explanatory variable.

Refer to Exercise 15.

(a) Carry out a significance test at the 伪=0.05level.

(b) Construct and interpret a 95%confidence interval for the difference between the population proportions. Explain how the confidence interval is consistent with the results of the test in part (a).

Final grades for a class are approximately Normally distributed with a mean of 76and a standard deviation of 8. A professor says that the top 10%of the class will receive an A, the next 20%a B, the next 40%a C, the next 20%a D, and the bottom 10%an F. What is the approximate maximum average a student could attain and still receive an F for the course?

(a) 70

(b)69.27

(c) 65.75

(d) 62.84

(e)57

Refer to Exercise16.

(a) Carry out a significance test at the 伪=0.05level.

(b) Construct and interpret a 95%confidence interval for the difference between the population proportions. Explain how the confidence interval is consistent with the results of the test in part (a).

A researcher wants to determine whether or not a five-week crash diet is effective over a long period of time. A random sample of 15 dieters is selected. Each person's weight is recorded before starting the diet and one year after it is concluded. Based on the data shown below (weight in pounds), can we conclude that the diet has a long-term effect, that is, that dieters managed to not regain the weight they lost? Include appropriate statistical evidence to justify your answer.
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