IMathAS-libretexts

5.7 Sleep habits of New Yorkers: New York is known as "the city that never sleeps". A random sample of 25 New Yorkers were asked how much sleep they get per night. Statistical summaries of these data are shown below. Do these data provide strong evidence that New Yorkers sleep less than 8 hours a night on average?

n	x̄	s	min	max
25	7.73	0.77	6.17	9.78

(a) Write the hypotheses in symbols.

Ho: μ = 8
Ha: μ < 8
Ho: μ = 8
Ha: μ > 8
Ho: μ = 8
Ha: μ ≠ 8

(b) Calculate the test statistic, T, and the degrees of freedom.
T = (please round to two decimal places)
There are degrees of freedom associated with this test.

(c) Find and interpret the p-value in this context. Drawing a picture may be helpful.
p = (please round to four decimal places)

(d) What is the conclusion of the hypothesis test?

Since p ≥ α we accept the null hypothesis
Since p<α we reject the null hypothesis and accept the alternative
Since p ≥ α we do not have enough evidence to reject the null hypothesis
Since p<α we fail to reject the null hypothesis
Since p ≥ α we reject the null hypothesis and accept the alternative

(e) If you were to construct a 90% confidence interval that corresponded to this hypothesis test, would you expect 8 hours to be in the interval?

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