Question

The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test. Test the claim that there is a linear correlation between hours of study and test scores, with 0.03 significance level and P-Value method.

Hours 6 7 5 9 4 10

Score 71 82 58 85 62 91

Answer 1

Answer: The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test. Test the claim that there is a linear correlation between hours of study and test scores, with 0.03 significance level and P-Value method.

Solution:

Let x be the number of hours studied.

And y be the test scores of students.

x	y	(x-x̄)^2	(y-)^2	x*y
6	71	0.694	14.694	3.194
7	82	0.028	51.361	1.194
5	58	3.361	283.361	30.861
9	85	4.694	103.361	22.028
4	62	8.028	164.694	36.361
10	91	10.028	261.361	51.194

∑x = 41

x̄ = 6.833

∑y = 449

= 74.833

SSx = ∑(x- x̄)^2 = 26.833

SSy = ∑(y-)^2 = 878.833

SSxy = ∑(x-x̄)(y-) = 144.833

Conclusion: Reject the null hypothesis, Ho. There is sufficient evidence to conclude that there is a linear correlation between hours of study and test scores, with 0.03 significance level.

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