Aplia: Student 7. Hypothesis tests with the Pearson correlation The rapld growth

Question

Aplia: Student 7. Hypothesis tests with the Pearson correlation The rapld growth of video game popularity has generated concern among pradtitioners, parents, scholars and politicdans," wrote researchers Hope M. Curnmings and Blizabeth 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, 16107), 684-689.J Cunmings 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 82 teenage girls who play video games. You want to determine whether the amount of time girls spend playing video games is negatively correlated with the amount of time they interact with their parents, so you ask the girls to keep a log of their activities over a week's time. p denote the population Pearson correlation coefficient between the amount of time girls spend playing video games and the amount of time they interact with their parents. Your null hypothesis is and your altemative hypothesis is Your hypothesis test wit be test. The Pearson correlation coefficient between the amount of time girls spend playing video games and the time they interact with their parents in your sample 0.08. The test statistic for your hypotess test is t The value for the degrees of freedom you should use for your hypothesis test is Degrees of Freedom on the following Distributions tool to find the critical voluets). Use this value to set the Degroes of Freadom-8 Sessign ss:36 At a significance leval of 0.05, the critical valueis) far your hypothesis test is tare)

Explanation / Answer

null hypothesis : The amount of time girls spend playing video games and the amount time they interact with their parents are independent

Alternative hypothesis : the amount of time girls spend playing video games and the amount time they interact with their parents are not independent

T test for single correlation coefficient

T statistic =

T statistic

= r*sqrt(n-2) / sqrt(1 - r2)

= -0.08 * sqrt(80) / sqrt(1 - 0.082)

= -0.72

Degrees of freedom = n - 2 = 82 - 2 = 80

Critical values = -1.99, +1.99

Do not reject Null hypothesis

Second option is correct

i,e there is no linear relation .............

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