Question

In: Math

You are a researcher who wants to know if there is a relationship between variable Y...

You are a researcher who wants to know if there is a relationship between variable Y and variable X. You hypothesize that there will be a strong positive relationship between variable Y GPA and Variable X hours of sleep. After one semester, you select five students at random out of 200 students who have taken a survey and found that they do not get more than 5 hours of sleep per night. You select five more students at random from the same survey that indicates students getting at least seven hours of sleep per night. You want to see if there is a relationship between GPA and hours of sleep. Using a Pearson Product Correlation Coefficient statistic, determine the strength and direction of the relationship and determine if you can reject or fail to reject the HO:

Variable Y        Variable X    

2.5                      5               

3.4                      8                

2.0                      4               

2.3                     4.5              

1.6                     3     

3.2                     6

2.8                     7

3.5                     7.5

4.0                     6.5

3.8                     7

Solutions

Expert Solution

S.No X Y (x-x̅)2 (y-y̅)2 (x-x̅)(y-y̅)
1 5 2.5 0.7225 0.1681 0.3485
2 8 3.4 4.6225 0.2401 1.0535
3 4 2 3.4225 0.8281 1.6835
4 4.5 2.3 1.8225 0.3721 0.8235
5 3 1.6 8.1225 1.7161 3.7335
6 6 3.2 0.0225 0.0841 0.0435
7 7 2.8 1.3225 0.0121 -0.1265
8 7.5 3.5 2.7225 0.3481 0.9735
9 6.5 4 0.4225 1.1881 0.7085
10 7 3.8 1.3225 0.7921 1.0235
Total 58.5 29.1 24.5250 5.7490 10.2650
Mean 5.850 2.910 SSX SSY SXY
correlation coefficient r= Sxy/(√Sxx*Syy)               = 0.8645

since correlation coefficient is positive and >0.70 ,  correlation is strong and positive.

since test statistic falls in rejection region we reject null hypothesis

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