Question

Aa Aa 7. Hypothesis tests with the Pearson correlation "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 82 teenage boys who play video games. You want to determine whether the amount of time boys spend playing video games is negatively correlated with the amount of time they interact with their parents, 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 interact with their parents. Your null hypothesis is and your alternative hypothesis is . Your hypothesis test will be test. The Pearson correlation coefficient between the amount of time boys spend playing video games and the time they interact with their parents in your sample is r = -0.08. The test statistic for your hypothesis test ist 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 value(s). Use this value to set the

Answer 1

1.Null hypothesis

H_o: or amount of tome spent on video games and spent on interaction with parents is uncorrelated.

p=0

2.Alternative hypothesis

H₁:$\rho<0$ or amount of tome spent on video games and spent on interaction with parents is negatively correlated.

3.We will use t-test of population correlation coeffiecient.

4.test-statistic:

The corresponding t-statistic to test for the significance of the correlation is:

$t = r\sqrt{ \frac{n-2}{1-r^2}} = -0.08\sqrt{ \frac{ 82-2}{1--0.08^2}} = -0.718$

5.degrees of freedom=The sample size is n=82, so then the number of degrees of freedom is df=n−2=82−2=80

6.critical value tc=1.6641

7.since |t|=0.718<tc=1.6641

also,

The p-value is computed as follows:

p=Pr(t80​<−0.718)=0.2375

Since we have that p=0.2375≥0.05, it is concluded that the null hypothesis H0​ is not rejected.

8.you will accept the null hypothesis and we do not conclude that there is a significant negative correlation between the amount of time boys spent on video games and the amount of time spent in interaction with parents.

9.option (A) there is no linear relationship between the time spent by boys on video games and the time in interaction with parents is correct.

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