Question

Researchers claim that getting a good nights sleep has an effect on test scores. A sample of 12 student’s grades were recorded for two exams, one for which they got a a full eight hours of sleep and one for which they only got 4 hours of sleep. Using a 0.05 level of significance, test the claim that the sleep has an effect on exam scores.
(a) State the claim, null hypothesis, and alternative hypothesis.
Claim: H0: H1:
(b) Given a test statistic of t = −1.2. What tail is the test? Find the P-value obtained from this test statistic and state the conclusion of the hypothesis test.

Tailed: p−value: Conclusion

Answer 1

a) Let us denote the difference

d = score for which they got a a full eight hours of sleep - score for whichthey only got 4 hours of sleep

Let denotes the mean difference in hours of sleep.

Null hypothesis

Alternative hypothesis

b) The value of test statistic t = -1.2

and degrees of freedom = sample size -1 = 12 - 1 = 11

P-value

Since P-value > 0.05, so we fail to reject the null hypothesis at 0.05 level of significance and there is not sufficient evidence to support the claim that the sleep has an effect on exam scores.