Question
In: Statistics and Probability
Randomly selected students in a statistics class were asked to report the number of hours they...
Randomly selected students in a statistics class were asked to report the number of hours they slept on weeknights and on weekends. At α = 0.05. Can it be claimed that the scores on 2 tests are correlated on 0.01 significance level?
Student #: 1 2 3 4 5 6 7 8
Test 1: 67 88 76 88 91 95 79 71
Test 2: 69 78 76 84 86 96 70 68
Solutions
Expert Solution
| null hypothesis: Ho: ρ | = 0 | ||
| Alternate Hypothesis: Ha: ρ | ≠ 0 | ||
| 0.01 level,two tail test and n-2= 6 df, critical t=3.707 | |||
| Decision rule: reject Ho if absolute value of test statistic |t|>3.707 | |||
| correlation coefficient r= | Sxy/(√Sxx*Syy) =623.375/√(712.875*671.88) = | 0.9007 | |
| test stat t= | r*(√(n-2)/(1-r2))= | 0.9007*√((8-2)/(1-0.9007^2)) =5.0780 | |
| since test statistic falls in rejection region we reject null hypothesis | ||||
| we have sufficient evidence to conclude that the scores on 2 tests are correlated | ||||
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