"The rapid growth of video game popularity has generated concern among practitioners, parents, scholars 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 of 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), 684-689.]

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 homework, or playing sports.

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 Pearson correlation coefficient 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 population Pearson 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.

The test statistic for your hypothesis test is t = ____________ .

The value for the degrees of freedom you should use for your hypothesis test is ___________ . Use this value to set the Degrees of Freedom on the following Distributions tool to find the critical value(s). (Note: Do not use the t-table to calculate the critical score as the answer requires an exact df.)

At a significance level of = 0.05, the critical value(s) for your hypothesis test is (are) __________ . 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?

___ The more time girls spend playing video games, the more time they spend playing with a sibling or peer.

___ When girls play video games, their siblings want to join them.

___ There is no linear relationship between the time girls spend playing video games and time spent playing with a sibling or peer.

___ This study found no linear relationship between the time girls spend playing video games and time spent playing with a sibling or peer.