PLEASE ONLY ANSWER IF YOU CAN FILL IN EACH BLANK, THANK YOU! Aa Aa 9. The Spearm

Question

PLEASE ONLY ANSWER IF YOU CAN FILL IN EACH BLANK, THANK YOU!

Aa Aa 9. The Spearman 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. In their study, Cummings and Vandewater measured the time adolescents spent playing video games as well as time spent doing other activities such as interacting with family and friends, reading or doing homework, or playing sports. [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.] After reading about the study conducted by Cummings and Vandewater, you decide to conduct a similar study among a sample of 8 teenage girls. You ask the girls to keep a log of their activities for a day. You want to test whether the amount of time girls spend playing video games is correlated with the amount of time they exercise. You realize that because some of the girls in your sample do not play video games at all, your data will have many zeroes for the amount of time they play video games You decide to use the Spearman correlation for the data. The first thing you do is convert the data to ranks. You convert the amount of time each girl plays video games by assigning the lowest rank to the four girls who don't play video games and the highest rank to those who play video games the most. The rank you assign to each of the four girls who don't play video games is The following table consists of the data for the 8 girls in your study. The data are sorted in order of the amount of time the girls spent playing video games. Fill in the missing ranks for the time spent playing video games and the ranks for the time spent exercising. Note that the time spent exercising is not sorted in order The following table consists of the data for the 8 girls in your study. The data are sorted in order of the amount of time the girls spent playing video games. Fi in the missing ranks for the time spent playing video games and the ranks for the time spent exercising. Note that the time spent exercising is not sorted in order.

Explanation / Answer

The rank you assign to each of the four girls who dont play vedio game is 2.5

Here 0 repeats 4 times,

Therefore, Rank of 0 is: (1 + 2 + 3 + 4)/4 = 10/4 = 2.5 ( For each 0's rank)

Simillarly, 80 repeats 2 times,

Therefore, rank of 80 is : (4 + 5) / 2 = 9/2 = 4.5 ( For each 80's rank)

The Pearson correlation formula applied to the ranks loses accuracy whe

Time spent Playing Vedio Games(x) Time Spent Exercising (y) Rank Time spent Playing Vedio Games: R(x) Rank Time Spent Exercising: R(y) d = R(x) - R(y) d^2 0 60 2.5 3 -0.5 0.25 0 112 2.5 6 -3.5 12.25 0 171 2.5 8 -5.5 30.25 0 80 2.5 4.5 -2 4 20 150 5 7 -2 4 33 80 6 4.5 1.5 2.25 82 45 7 2 5 25 126 28 8 1 7 49 Total 127

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