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? (Test at that 5\% significance level.)

n	x̄	s	min	max
25	7.77	0.72	6.17	9.78

(a) Write the hypotheses in symbols.

(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. (Round to four decimal places.)
The P-value is

(d) What is the conclusion of the hypothesis test? (Recall that the significance level α is 0.05.)

Since the P-value is not small, we do not have enough evidence to reject the null hypothesis.
Since the P-value is small, we fail to reject the null hypothesis.
Since the P-value is small, we reject the null hypothesis and accept the alternative.
Since the P-value is not small, we reject the null hypothesis and accept the alternative.
Since the P-value is not small, we accept the null hypothesis.

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