9.6 Practice

Does Friday the 13th have an effect on people’s behavior? Researchers collected data on the number of shoppers at a random sample of 45 grocery stores on Friday the 6th and Friday the 13th in the same month. A dotplot of the difference in the number of shoppers at each store on these 2 days (Friday the 6th – Friday the 13th) is shown here. The mean difference is -46.5 and the standard deviation of the differences is 178.0.47

Do these data provide convincing evidence at the α = 0.05 level of a mean difference in the number of shoppers at grocery stores on these 2 days?

• Because the P-value of 0.087 > α = 0.05, we fail to reject H₀. We don't have convincing evidence of a difference in mean number of shoppers at grocery stores on these two days.

• Because the P-value of 0.087 > α = 0.05, we reject H₀. We have convincing evidence of a difference in mean number of shoppers at grocery stores on these two days.

• Because the P-value of 0.087 < α = 0.05, we fail to reject H₀. We don't have convincing evidence of a difference in mean number of shoppers at grocery stores on these two days.

• Because the P-value of 0.087 < α = 0.05, we reject H₀. We have convincing evidence of a difference in mean number of shoppers at grocery stores on these two days.

To compare the wear characteristics of two tire brands, two new Brand A tires are mounted on one side of each of 30 cars of the same model, while two new Brand B tires are mounted on the other side. Which side gets which brand is determined by flipping a coin. After 5000 miles of driving, the amount of wear is measured for each tire.

Decide whether you should use two-sample t procedures to perform inference about a difference in means or one-sample t procedures to perform inference about a mean difference. Explain your choice in each case.

• Two-sample t procedures, two separate random samples

• Two-sample t procedures, paired data (tires assigned to both sides of the car randomly)

• One-sample t procedures, two separate random samples

• One-sample t procedures, paired data (tires assigned to both sides of the car randomly)

To compare funding for men’s and women’s sports teams, researchers randomly select 100 colleges and record the amount of money spent on the men’s basketball program and the women’s basketball program at each college.

Decide whether you should use two-sample t procedures to perform inference about a difference in means or one-sample t procedures to perform inference about a mean difference. Explain your choice in each case.

• Two-sample t procedures, two separate random samples

• Two-sample t procedures, paired data (colleges)

• One-sample t procedures, two separate random samples

• One-sample t procedures, paired data (colleges)

Can listening to music while working increase productivity? A total of 20 factory workers agree to take part in a study to investigate this question. Researchers randomly assign 10 workers to do a repetitive task while listening to music and the other 10 workers to do the task in silence. They record the time it takes each worker to complete the task.

Decide whether you should use two-sample t procedures to perform inference about a difference in means or one-sample t procedures to perform inference about a mean difference. Explain your choice in each case.

• Two-sample t procedures, two randomized groups

• Two-sample t procedures, paired data (colleges)

• One-sample t procedures, two separate random samples

• One-sample t procedures, paired data (colleges)

Which of two brands of ski wax works better? To find out, researchers randomly assign 15 skiers to do a downhill race with one brand of wax and 15 different skiers to do a downhill race with the other brand of wax. Then researchers compare the average times of the skiers in the two groups.

Decide whether you should use two-sample t procedures to perform inference about a difference in means or one-sample t procedures to perform inference about a mean difference. Explain your choice in each case.

• Two-sample t procedures, two separate random groups

• Two-sample t procedures, paired data (colleges)

• One-sample t procedures, two separate random groups

• One-sample t procedures, paired data (colleges)