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Chapter 3: Q.20 (page 161)

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?

Short Answer

Expert verified

a). The correlation should be positive.

b). The value ofr=0.5653.

Step by step solution

01

Part(a) Step 1: Given Information

Data:

02

Part(a) Step 2: Explanation 

Women (x)is on the horizontal axis, and Men (y)is on the vertical axis.

03

Part(a) Step 3: Explanation

The scatterplot slopes upwards, indicating that the correlation should be positive.

Because the points do not appear to be on the same axis, the correlation should be less than卤1.

04

Part(b) Step 1: Given Information 

Data:

05

Part(b) Step 2: Explanation 

To find X路Y,X2and Y2as it was done in the table below.

06

Part (b) Step 3: Explanation 

Find the sum of every column to get:

鈭�X=396,鈭�Y=414,鈭�X路Y=27339,鈭�X2=26158,鈭�Y2=28598

To calculate the correlation coefficient, use the formula below.

localid="1649931991616" r=n路鈭�XY-鈭�X路鈭�Yn鈭�X2-鈭�X2路n鈭�Y2-鈭�Y2=6鈰�27339鈭�396鈰�4146鈰�26158鈭�3962鈰�6鈰�28598鈭�4142鈮�0.5653

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Most popular questions from this chapter

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.

Managing diabetes People with diabetes measure their fasting plasma glucose (FPG; measured in units of milligrams per milliliter) after fasting for at least 8 hours. Another measurement, made at regular medical checkups, is called HbA. This is roughly the percent of red blood cells that have a glucose

molecule attached. It measures average exposure to glucose over a period of several months. The table below gives data on both HbA and FPG for 18 diabetics five months after they had completed a diabetes education class.

(a) Make a scatterplot with HbA as the explanatory variable. There is a positive linear relationship, but it is surprisingly weak.

(b) Subject 15 is an outlier in the y-direction. Subject 18 is an outlier in the x-direction. Find the correlation for all 18 subjects, for all except Subject 15 and

for all except Subject 18 Are either or both of these subjects influential for the correlation? Explain in simple language why r changes in opposite directions when we remove each of these points.

(c) Add three regression lines for predicting FPG from HbA to your scatterplot: for all 18 subjects, for all except Subject 15 and for all except Subject 18

Is either Subject 15 or Subject 18 strongly influential for the least-squares line? Explain in simple language what features of the scatterplot explain the degree of influence.

Outsourcing by airlines Exercise 5 (page 158) gives data for 14 airlines on the percent of major maintenance outsourced and the percent of flight delays blamed on the airline.

(a) Make a scatterplot with outsourcing percent as x and delay percent as y Hawaiian Airlines is a high outlier in the y-direction. Because several other airlines have similar values of x the influence of this outlier is unclear without actual calculation.

(b) Find the correlation rwith and without Hawaiian Airlines. How influential is the outlier for correlation?

(c) Find the least-squares line for predicting yfrom xwith and without Hawaiian Airlines. Draw both lines on your scatterplot. Use both lines to predict the percent of delays blamed on an airline that has outsourced 76%of its major maintenance. How influential is the outlier for the least-squares line?

Beer and blood alcohol The example on page 182describes a study in which adults drank different amounts of beer. The response variable was their blood alcohol content (BAC). BAC for the same amount of beer might depend on other facts about the subjects. Name two other variables that could account for the fact that r2=0.80.

A government report looked at the amount borrowed for college by students who graduated in 2000and had taken out student loans.12 The mean amount was x=\(17,776and the standard deviation was sx=\)12,034. The median was\(15,532and the quartiles were Q1=\)9900and Q3=\(22,500.

(a) Compare the mean and the median. Also compare the distances of Q1 and Q3 from the median. Explain why both comparisons suggest that the distribution is right-skewed.

(b) The right-skew pulls the standard deviation up. So a Normal distribution with the same mean and standard deviation would have a third quartile larger than the actual Q3.Find the third quartile of the Normal distribution with渭=\)17,776and 蟽=\(12,034and compare it withQ3=\)22,500.
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