Module 8 ReviewAP Statistics

1. Even though Puerto Rico is a territory of the United States there are many cultural differences between the states on the continent and the island of Puerto Rico. These differences include the way consumers handle problems with purchases. Two researchers surveyed owners of VCRs in the Northeast United States and in Puerto Rico. They asked those who had experienced problems with their VCRs whether they complained. The results are given in the table below.

Complained States Puerto Rico

No 70 27

Yes 420 103

a) Do these data provide good evidence of an association between complaints and location?

b) Which cell contributes most to the chi-square test statistic?

2. In the paper "Color Association of Male and Female Fourth-Grade School Children" (J. Psych., 1988, 383–8), children were asked to indicate what emotion they associated with the color red. The analysis is as follows:

Frequency| Row |anger |happy |love |pain | ---------+--------+--------+--------+--------+ f | 27 | 19 | 39 | 17 | ---------+--------+--------+--------+--------+ m | 34 | 12 | 38 | 28 | ---------+--------+--------+--------+--------+

a) What proportion of those surveyed associate anger with the color red?

b) Using the data above, what proportion of females associate love with the color red?

c) Suppose we wish to test the null hypothesis that there are no differences among the proportion of males and the proportion of females choosing each of the emotions associated with the color red. Under the null hypothesis, what is the expected number of males that would select “happy”?

d) What are the appropriate degrees of freedom for the chi-square test statistic?

e) Is there significant evidence that the emotion associated with the color red is dependent on gender?

3. Suppose we wish to create a graphical display of the proportion of all above average readers that wear glasses and do not wear glasses, respectively. Which graphical displays is best suited to this purpose?

4. A recent estimate by a large distributor of gasoline claims that 60% of all cars stopping at their service stations chose unleaded gas and that super unleaded and regular were each selected 20% of the time. In order to check the validity of these proportions, a study was conducted of cars stopping at the distributor's service stations in a large city. The results were as follows:

Gasoline Selected Regular Unleaded Super Unleaded 51 261 88

Carry out a significance test of the distributor’s claim.

5. Cars typically advertise their horsepower ratings and expected gas mileage (mpg). Below is the Minitab regression output for data on 120 2007 vehicles.

a. Write the equation of the LSRL.

b. Interpret the slope in the context of the problem.

c. Interpret the y-intercept in the context of the problem.

d. Compute the 96% confidence interval for the slope parameter. Compute the margin of error that should be used. Assume that conditions for inference are satisfied.

6. Sixteen student volunteers at Ohio State University drank a randomly assigned number of cans of beer. Thirty minutes later, a police officer measured their blood alcohol content (BAC). Here are the results:

Predictor Coef StDev T P

Constant 46.868 2.981 15.72 0.000

horsepower -0.08380 0.01325 -6.32 0.000

a. Write the slope of the least squares regression line.

b. What is the y-intercept of the least squares regression line?

c. Suppose we wish to test the claim that BAC increases with the numbers of beers consumed. Perform a significance test to test this claim. Be sure to show all steps. Assume the conditions for inference are satisfied.