Question

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Assume that a researcher is interested in finding out the relationship between standardized test scores and...

  1. Assume that a researcher is interested in finding out the relationship between standardized test scores and household income. Seven participants have been randomly selected and their ACT Composite score and household income are reported. By performing a test, can you conclude that there is a significant relationship between household income and ACT Composite score? State your null and alternative hypotheses. Please show all of the required steps. Use the data in the table below. Assume α = .05 (20 points)

Income (in thousands)

ACT Composite score

30

16

21

18

24

18

59

21

55

23

105

25

35

26

Solutions

Expert Solution

S.No X Y (x-x̅)2 (y-y̅)2 (x-x̅)(y-y̅)
1 30 16 289.0000 25.0000 85.0000
2 21 18 676.0000 9.0000 78.0000
3 24 18 529.0000 9.0000 69.0000
4 59 21 144.0000 0.0000 0.0000
5 55 23 64.0000 4.0000 16.0000
6 105 25 3364.0000 16.0000 232.0000
7 35 26 144.0000 25.0000 -60.0000
Total 329 147 5210.0000 88.0000 420.0000
Mean 47.000 21.000 SSX SSY SXY

since test statistic does not falls in rejection region we fail to reject null hypothesis
we do not have have sufficient evidence to conclude that, t there is a significant relationship between household income and ACT Composite score

milcah answered 1 year ago
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