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
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.
Researchers claim that getting a good nights sleep has an effect on test scores. A sample...
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