Falowng is a partial table of critical values f the sample Pearson correlation r

Question

Falowng is a partial table of critical values f the sample Pearson correlation r for the test of = o. 8. Hypothesis tests with the Pearson correlation Ma Aa Level of Significance for the One-Tailed Test Level of significance for the Two-Tailed Test "The rapid growth af video game popularity has generated concern among practitioners, parents, schalars and politicians," wrote researchers Hope M. Cummings and Elizabeth A. Vandewater. "Particularly during adolescence, when social interactions and academic success lay the groundwork for health in adulthood, there is concern that video games will interfere with the development af skills needed to make a successful transition to adulthood. [Source: Cummings, H., & Vandewater, E. (2007). Relation of adolescent video game play to time spent in other activities. Archives of Pediatrics & Adolescent Medicine, 161(7), 634-639.] 0.05 0.025 0.01 0.005 0.10 0.05 0.02 0.01 df 0.231 0,273 0.322 0.354 70 80 90 100 0.195 0,232 0.274 0,302 0.183 D.217 0.257 0.283 0.173 0.205 0.242 0,267 0.164 0.195 0.230 0.254 Cummings and Vandewater measured the time adolescents spent playing video games and the time they spent doing other activities, such as interacting with family and friends, reading or doing hamework, ar playing sports Suppose you decide to conduct a similar study among a random sample of 62 teenage boys who play video games You want to determine whether the amount of time boys spend playing video games is positively correlated with the amount of time they play with a sibling or peer, so you ask the boys to keep a log of their activities over week's time. With = 0.05, the tabe lists a critical value of hypothesis and spend playing vided games and the amount of time they play with a sbling or peer, with this critical value you will fal to reect the null condlude that there is a significant positive correlation between the amount of time boys Let denote the population Pearson correlation between the amount of time boys spend playing video games and the amount of time they play with a sibling or peer. Your null hypothesis is hypothesis is cannot and your altemative Given your is the most appropriate interpretation of your result? Your hypothesis test will be a left-tailedHp: p s0 Ho: r=0 O The more time boys spend playing video games, the more time they spend playing with a sibling or peer O There is no linear relationship between the time bays spend playing video games and time spent playing with The Pearson correlation uetween the amount of tirne boys spend playing sibling or peer in your sample is 0.19. As a test statistic for the hypothesis test of = 0, the sample Pearson correlation r a sibling or peer When boys play video games, their sblings want to join them This study found no linear relationship between the time bays spend playing video games and time spent playing with a sibling or peer the time they play with a 60 degrees of freedom. 61 59 70

Explanation / Answer

1. since here we want to determine if there exist a strong positive relationship between time they spend on video game and the time they spend in playing with their siblings it becomes a one tail test and so

Here the null hypothesis i.e. Ho is  true correlation is greater then & equal to 0 i.e. >=0

so., the alternative hypotheisi Ha:  <0 . The hypothesis test will be right tailed test since we are concerned with the strong positive relationship

2. degrees of freedom = n-2 = 62(number of teen age boys)-2 =60

3. Since we are concerned with the significance of 0.05 and this is a one tail test the critical value at one tail's 0.05 with df=60 is 0.211 while the r vale we have got here is 0.19 (given in the previous question) which is less than t critical and so here we fail to reject Ho and so we can say that we cannot conclude that there is strong positive relationship

4. the most appropreate interpretetaion is ans (d)

Although we are bound to answer 4 questions only I have answered all your questions. Pls upvote the ans if it has really helped you. Good Luck!!

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