**Understanding the Impact of Video Game Play on Adolescents' Activities**"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 girls who play video games. You want to determine whether the amount of time girls spend playing video games is correlated with the amount of time they exercise, so you ask the girls to keep a log of their activities over a week’s time.Let ρ denote the population Pearson correlation coefficient between the amount of time girls spend playing video games and the amount of time they exercise. 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 exercise in your sample is r = -0.52.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). **t Distribution**- **Degrees of Freedom = 51**(Graph Description: A t-distribution graph is displayed, which is a symmetrical, bell-shaped curve centered around 0 on the x-axis. The x-axis ranges from -3.0 to 3.0.)---At a significance level of α = 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 correlation between the amount of time girls 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 girls spend playing video games, the more time they spend exercising.- ☐ This study found no linear relationship between the time girls spend playing video games and time spent exercising.- ☐ Playing video games takes away from the time girls spend exercising.- ☐ The more time girls spend playing video games, the less time they spend exercising.

Given Information: Sample size (n) = 52 Significance level α = 0.05 r=-0.52 To determine whether the amount of time girls spend playing video games is correlated with the amount of time they exercise. State the hypothesis as follows: Null Hypothesis: H0:ρ=0 i.e., there is no association or relationship between the two variables. In other words, there is no correlation between the two variables. (amount of time girls spend playing video games and amount of time they exercise.) Alternative Hypothesis: Ha:ρ≠0 i.e., there is a significant association between the two variables. This is a two tailed test.Test statistic is given by the formula: t=rn-21-r2 Substitute the given values in the formula: t=-0.5252-21--0.522=-3.6770.8542≈-4.305 Thus, the value of the test statistic is -4.305 Degrees of freedom = n-2=52-2=50 Using a table of critical values of Pearson Correlation, for a two tailed test at 0.05 significance level and 50 degrees of freedom, the critical values are: -0.273 and +0.273 Decision Rule: If computed r value is greater than the r tabular value or if r value is less than the critical value and test value falls in the critical region, reject null hypothesis. Since, -0.52 is less than the critical value -0.273, we reject the null Hypothesis. The correlation coefficient is significant. There is sufficient evidence to conclude that there is a significant correlation between the amount of time girls spend playing video games and amount of time they exercise. The more time girls spend playing video games, the less time they spend exercising.

Math

Statistics

The population Pearson correlation coefficient between the amount of time girls 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 = 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).

The population Pearson correlation coefficient between the amount of time girls 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 = 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).

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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