Question
In: Math
Assume that a researcher is interested in finding out the relationship between standardized test scores and...
- 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 |
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