t Distribution Degrees of Freedom = 51 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 At a significance level of a = reject 0.05, the critical value(s) for your hypothesis test is (are) ±2.009 the null hypothesis and can With this critical value you will conclude that there is a significant correlation between the amount of time boys spend playing video games and the amount of time they exercise. Given your conclusion, what is the most appropriate interpretation of your result? The more time boys spend playing video games, the more time they spend exercising. This study found no linear relationship between the time boys spend playing video games and time spent exercising. Playing video games takes away from the time boys spend exercising. The more time boys spend playing video games, the less time they spend exercising. "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 52 teenage boys who play video games. You want to determine whether the amount of time boys spend playing video games is correlated with the amount of time they exercise, so you ask the boys to keep a log of their activities over a week's time. Let p denote the population Pearson correlation coefficient between the amount of time boys spend playing video games and the amount of time they exercise. Your null hypothesis is H: p = 0 and your alternative hypothesis is H.: p < 0 Your hypothesis test will be a two-tailed test. The population Pearson correlation coefficient between the amount of time boys spend playing video games and the time they exercise in your sample is r = -0.52. The test statistic for your hypothesis test is t = -4.30 The value for the degrees of freedom you should use for your hypothesis test is 50 following Distributions tool to find the critical value(s). Use this value to set the Degrees of Freedom on the

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