7.7 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. The point estimate suggests New Yorkers sleep less than 8 hours a night on average. Is the

result statistically signicant?

n x s min max

25 7.73 0.77 6.17 9.78

(a) Write the hypotheses in symbols and in words.

(b) Check conditions, then calculate the test statistic, T, and the associated degrees of freedom.

(c) Find and interpret the p-value in this context. Drawing a picture may be helpful.

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

(e) If you were to construct a 90% condence interval that corresponded to this hypothesis test, would you

expect 8 hours to be in the interval?