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

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=		S_xy/(√S_xxS_yy) =623.375/√(712.875671.88) =	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

orchestra answered 2 years ago

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