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Chapter 3: Q.24 (page 162)

Data on dating Refer to Exercise 20.

(a) How would r change if all the men were 6 inches shorter than the heights given in the table? Does the correlation tell us if women tend to date men taller than themselves?

(b) If heights were measured in centimeters rather than inches, how would the correlation change? (There are 2.54centimeters in an inch.)

Short Answer

Expert verified
  1. The linear correlation coefficient r will remain unchanged.
  2. The relationship would remain unchanged.

Step by step solution

01

Part (a) Step 1: Given Information 

Data:

02

Part (a) Step 2: Explanation

The correlation between mean heights and women's heights will remain unchanged if all men's heights vary by the same amount, and therefore the linear correlation rwill remain unchanged.

03

Part (b) Step 1: Given Information 

Data:

04

Part (b) Step 2: Explanation 

The correlation would not change since it is unit-independent.

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Most popular questions from this chapter

Bird colonies One of nature鈥檚 patterns connects the percent of adult birds in a colony that return from the previous year and the number of new adults that join the colony. Here are data for 13colonies of sparrow-hawks:4

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(d) Interpret the value of s in this setting.

When we standardize the values of a variable, the distribution of standardized values has a mean 0and a standard deviation 1Suppose we measure two variables Xand Yon each of several subjects. We standardize both variables and then compute the least-squares regression line. Suppose the slope of the least-squares regression line is 鈭�0.44We may conclude that

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Data on dating A student wonders if tall women tend to date taller men than do short women. She measures herself, her dormitory roommate, and the women in the adjoining rooms. Then she measures the next man each woman dates. Here are the data (heights in inches):

(a) Make a scatterplot of these data. Based on the scatterplot, do you expect the correlation to be positive or negative? Near 卤1or not?

(b) Find the correlation r step-by-step. First, find the mean and standard deviation of each variable. Then find the six standardized values for each variable. Finally, use the formula for r. Do the data show that taller women tend to date taller men?
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