7. A study of youth video-game culture was conducted in schools throughout British Columbia, Canada. Part of the study focused on the differences in academic performance between "heavy" players and "light" players of video games: heavy players defined as spending more than 7 hours per week on the games; light players defined as spending less than 3 hours per week gaming.

• A sample of 240 "heavy" users had an average GPA of 2.7, with a standard deviation of 0.7.
• A sample of 320 "light" users had an average GPA of 3.2, with a standard deviation of 0.6.

a. Build a 90% confidence interval estimate of the difference in average GPA for the two populations of "heavy" and "light" gamers.

b. Test the hypothesis that mean GPA between heavy and light game players are equal at the a = 5% significance level. What do you find?

8. Two proposed advertising campaigns themes for a new product are being evaluated for effectiveness. A random sample of 120 consumers is exposed to theme A, and another sample of 100 consumers is exposed to theme B. The study asks each customer whether they have a positive opinion of the product.

• 78% of the theme A participants said, yes, they have a positive opinion about the product.
• 64% of the theme B participants said, yes, they have a positive opinion about the product.

Is there enough evidence to support the claim that theme A is a more effective campaign than theme B, with an a = 5% level of significance?

9. In a test of running shoes, German sporting goods manufacturer, Derrunningzmitdershoessenhoffer, randomly selected 8 amateur runners to test two of its new shoe designs. The table shows how long the test shoes lasted before they were no longer usable.

Wear Time in Weeks

Runner

1

2

3

4

5

6

7

8

Design 1

15.6

17.6

10.3

9.4

13.4

13.5

14.7

20.6

Design 2

14.7

16.1

8.0

9.0

15.3

10.2

15.2

18.3

Test the null hypothesis that there is no difference in average life for the two shoes, using a = 5%.