(20 points) Listed below are the hours of aerobic exercise and hours of sleep pe

Question

(20 points) Listed below are the hours of aerobic exercise and hours of sleep per week of ten randoml Rank Correlation Test to determine whether a significant rank correlation exists between the hours of aerobic exercise per week and hours of sleep per week. Points will be deducted for steps that are incomplete or missing y selected students. Using an = 0.05 significance level, conduct the formal Hours Of Hours Of Exercise 5.25 17.5 Sleep 12.25 14 10.50 8.75 3.50 15.75 19.25 42 63 70 56 59.5 52.5 45.5 49 66.5

Explanation / Answer

H0 :   = 0

Ha :   0

The rank table with difference and sum of difference square is given below.

Here   = 1 - 6 * di2 /n(n2-1)

   = 1 - 6* 52/ [10 * (102-1)]

= 1 - 6* 52 /(10 * 99) = 0.6848

THe t value for the correlation

t = sqrt[(n-2)/ (1 - 2]

t = 0.6848 * sqrt [ 8/ ( 1- 0.68482)

t = 2.6579

Here tcritical for dF = 10 - 2 = 8 and alpha = 0.05

tcritical  = 2.306

so here t > tcritical   so we can reject the null hypothesis and can conclude that there is significant rank coefficient exists.

Hours of exercise Rank Hours of Sleep Rank Difference d^2 5.25 2 42 1 1 1 17.5 9 63 7 2 4 7 3 70 9 -6 36 12.25 6 56 5 1 1 14 7 59.5 6 1 1 10.5 5 52.5 4 1 1 8.75 4 45.5 2 2 4 3.5 1 49 3 -2 4 15.75 8 66.5 8 0 0 19.25 10 77 10 0 0 sum 52

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