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Chapter 3: Q 22. (page 174)

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 dorm rooms. Then she measures the next man each woman dates. Here are the data (heights in inches):

a. Make a scatterplot of these data. Describe what you see.

b. Find the correlation r step by step, using the formula on page 166. Explain how your value for r matches your description in part (a).

Short Answer

Expert verified

Part (a) It appears that there is a positive correlation between women and men.

Part (b) The value of r is 0.5653

Step by step solution

01

Part (a) Step 1: Given information

02

Part (a) Step 2: Explanation

There are the following steps into excel.

Put the data into excel sheet.

Click on

Insert.

Select the data set.

Click on

Scatter

It appears that there is a positive correlation between women and men.

03

Part (b) Step 1: Calculation

The sample size (n)is 6

The linear correlation coefficient (r)can be calculated as:

r=n(危xy)鈭�(危x)(危y)n危x2(危x)2(n危y2(危y)2)=6(27339)鈭�(396)(414)6(26158)-(396)26(28598)鈭�4142=0.5653

Thus, the value of ris 0.5653

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Most popular questions from this chapter

By looking at the equation of the least-squares regression line, you can see that the correlation between height and arm span is

a. greater than zero.

b. less than zero.

c. 0.93.

d. 6.4.

e. Can鈥檛 tell without seeing the data.

When we standardize the values of a variable, the distribution of standardized values has a mean of 0 and a standard deviation of 1. Suppose we measure two variables X and Y on 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 20.44. We may conclude that

a. the intercept will also be 鈭�0.44.

b. the intercept will be 1.0.

c. the correlation will be 1/鈭�0.44.

d. the correlation will be 1.0.

e. the correlation will also be 鈭�0.44.

In a scatterplot of the average price of a barrel of oil and the average retail price of a gallon of gas, you expect to see

a. very little association.

b. a weak negative association.

c. a strong negative association.

d. a weak positive association.

e. a strong positive association.

The scatterplot shows the relationship between the number of people per television set and the number of people per physician for 40 countries, along with the least-squares regression line. In Ethiopia, there were 503 people per TV and 36,660 people per doctor. Which of the following is correct?

a. Increasing the number of TVs in a country will attract more doctors.

b. The slope of the least-squares regression line is less than 1.

c. The correlation is greater than 1.

d. The point for Ethiopia is decreasing the slope of the least-squares regression line.

e. Ethiopia has more people per doctor than expected, based on how many people it has per TV.

Long strides The scatterplot shows the relationship between x = height of a student (in inches) and y = number of steps required to walk the length of a school hallway, along with the regression line y^=113.6鈭�0.921x

a. Calculate and interpret the residual for Kiana, who is 67 inches tall and took 49 steps to walk the hallway.

b. Matthew is 10 inches taller than Samantha. About how many fewer steps do you expect Matthew to take compared to Samantha?
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