Question

Suppose you decide to conduct a similar study among a random sample of 62 teenage girls who play video games. You want to determine whether the amount of time girls spend playing video games is positively correlated with the amount of time they play with a sibling or peer, so you ask the girls to keep a log of their activities over a week’s time. Let ? denote the population correlation between the amount of time girls spend playing video games and the amount of time they play with a sibling or peer. Your null hypothesis is and your alternative hypothesis is . Your hypothesis test will be test. The correlation coefficient between the amount of time girls spend playing video games and the time they play with a sibling or peer in your sample is r = 0.19. As a test statistic for the hypothesis test of ? = 0, the sample correlation coefficient r has degrees of freedom. Following is a partial table of critical values of the sample correlation coefficient r for the test of ? = 0. Level of Significance for the One-Tailed Test 0.05 0.025 0.01 0.005 Level of Significance for the Two-Tailed Test 0.10 0.05 0.02 0.01 df 50 0.231 0.273 0.322 0.354 60 0.211 0.250 0.295 0.325 70 0.195 0.232 0.274 0.302 80 0.183 0.217 0.257 0.283 90 0.173 0.205 0.242 0.267 100 0.164 0.195 0.230 0.254 With ? = 0.05, the table lists a critical value of . With this critical value you will the null hypothesis and conclude that there is a significant positive correlation between the amount of time girls spend playing video games and the amount of time they play with a sibling or peer. Given your conclusion, what is the most appropriate interpretation of your result? This study found no linear relationship between the time girls spend playing video games and time spent playing with a sibling or peer. There is no linear relationship between the time girls spend playing video games and time spent playing with a sibling or peer. When girls play video games, their siblings want to join them. The more time girls spend playing video games, the more time they spend playing with a sibling or peer.

Suppose you decide to conduct a similar study among a random sample of 62 teenage girls who play video games. You want to determine whether the amount of time girls spend playing video games is positively correlated with the amount of time they play with a sibling or peer, so you ask the girls to keep a log of their activities over a week’s time.

Let ? denote the population correlation between the amount of time girls spend playing video games and the amount of time they play with a sibling or peer. Your null hypothesis is and your alternative hypothesis is . Your hypothesis test will be test.

The correlation coefficient between the amount of time girls spend playing video games and the time they play with a sibling or peer in your sample is r = 0.19. As a test statistic for the hypothesis test of ? = 0, the sample correlation coefficient r has degrees of freedom.

Following is a partial table of critical values of the sample correlation coefficient r for the test of ? = 0.

Level of Significance for the One-Tailed Test 0.05 0.025 0.01 0.005
Level of Significance for the Two-Tailed Test 0.10 0.05 0.02 0.01
df
50 0.231 0.273 0.322 0.354
60 0.211 0.250 0.295 0.325
70 0.195 0.232 0.274 0.302
80 0.183 0.217 0.257 0.283
90 0.173 0.205 0.242 0.267
100 0.164 0.195 0.230 0.254

With ? = 0.05, the table lists a critical value of . With this critical value you will the null hypothesis and conclude that there is a significant positive correlation between the amount of time girls spend playing video games and the amount of time they play with a sibling or peer.

Given your conclusion, what is the most appropriate interpretation of your result?

This study found no linear relationship between the time girls spend playing video games and time spent playing with a sibling or peer.
There is no linear relationship between the time girls spend playing video games and time spent playing with a sibling or peer.
When girls play video games, their siblings want to join them.
The more time girls spend playing video games, the more time they spend playing with a sibling or peer.

Suppose you decide to conduct a similar study among a random sample of 62 teenage girls who play video games. You want to determine whether the amount of time girls spend playing video games is positively correlated with the amount of time they play with a sibling or peer, so you ask the girls to keep a log of their activities over a week’s time.

Let ? denote the population correlation between the amount of time girls spend playing video games and the amount of time they play with a sibling or peer. Your null hypothesis is and your alternative hypothesis is . Your hypothesis test will be test.

The correlation coefficient between the amount of time girls spend playing video games and the time they play with a sibling or peer in your sample is r = 0.19. As a test statistic for the hypothesis test of ? = 0, the sample correlation coefficient r has degrees of freedom.

Following is a partial table of critical values of the sample correlation coefficient r for the test of ? = 0.

Level of Significance for the One-Tailed Test 0.05 0.025 0.01 0.005
Level of Significance for the Two-Tailed Test 0.10 0.05 0.02 0.01
df
50 0.231 0.273 0.322 0.354
60 0.211 0.250 0.295 0.325
70 0.195 0.232 0.274 0.302
80 0.183 0.217 0.257 0.283
90 0.173 0.205 0.242 0.267
100 0.164 0.195 0.230 0.254

With ? = 0.05, the table lists a critical value of . With this critical value you will the null hypothesis and conclude that there is a significant positive correlation between the amount of time girls spend playing video games and the amount of time they play with a sibling or peer.

Given your conclusion, what is the most appropriate interpretation of your result?

This study found no linear relationship between the time girls spend playing video games and time spent playing with a sibling or peer.
There is no linear relationship between the time girls spend playing video games and time spent playing with a sibling or peer.
When girls play video games, their siblings want to join them.
The more time girls spend playing video games, the more time they spend playing with a sibling or peer.

Added by Keith P.

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