Question

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

Answer 1

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