Question

A "sleep habits" survey answered by 23 randomly selected New Yorkers contained the question "How much sleep do you get per night?" The sample average was 7.75 hours, with a corresponding sample standard deviation of 0.8 hours. Conduct a hypothesis test to see if there is evidence that New Yorkers (who live, after all, in "the city that never sleeps") on average get less than 8 hours of sleep per night, using α=0.05.

a. The t test statistic is:  
Round your answer to 3 decimal places

b. What is probability that we would obtain a test statistic at least this extreme if the population mean sleep time for New Yorkers was not less than 8 hours per night?

Hint: the phrasing of this question is based on the definition of a particular statistic. Round your answer to 3 decimal places

c. Using a level of significance of 0.05, the data  ---Select--- provides statistically significant does not provide statistically significant evidence to suggest that New Yorkers on average get less than 8 hours of sleep per night. A "sleep habits" survey answered by 23 randomly selected New Yorkers contained the question "How much sleep do you get per night?" The sample average was 7.75 hours, with a corresponding sample standard deviation of 0.8 hours. Conduct a hypothesis test to see if there is evidence that New Yorkers (who live, after all, in "the city that never sleeps") on average get less than 8 hours of sleep per night, using α=0.05.

a. The t test statistic is:  
Round your answer to 3 decimal places

b. What is probability that we would obtain a test statistic at least this extreme if the population mean sleep time for New Yorkers was not less than 8 hours per night?

Hint: the phrasing of this question is based on the definition of a particular statistic. Round your answer to 3 decimal places

c. Using a level of significance of 0.05, the data  ---Select--- provides statistically significant does not provide statistically significant evidence to suggest that New Yorkers on average get less than 8 hours of sleep per night.

Answer 1

We have to test, H0: = 8 against H1: < 8,

where denotes the average hours of sleep per night.

The test-statistic is, T = , where, = 7.75, = 8, s = 0.8, n = 23

Thus, T = - 1.4987. (Ans).

Under H0, T ~ t-distribution with (n-1) d.f. i.e. 22 d.f.

The p-value is = P(T < - 1.4987) = 0.0741. (Ans).

Since, p-value > level of significance = 0.05, we fail to reject H0. Hence, the data does not provide significant evidence to reject H0.