Sleep habits of New Yorkers: New York is known as \"the city that never sleeps\"

Question

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? Use a significance level of 5%. USE YOUR TI CALCULATOR Write the hypotheses in symbols. Ho:mu=8 Ha:mu8 Ho:mu=8 Ha:muinequlity8 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. Find the P-value in this context. P= (please round to four decimal places) What is the conclusion of the hypothesis test? Since p greater than or equal to alpha we do not have enough evidence to reject the null hypothesis. These data provide evidence that New Yorkers sleep less than 8 hours a night on average Since p

Explanation / Answer

Set Up Hypothesis
Null, H0: U=8
Alternate, H1: U<8
Test Statistic
Population Mean(U)=8
Sample X(Mean)=7.73
Standard Deviation(S.D)=0.77
Number (n)=25
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =7.73-8/(0.77/Sqrt(25))
to =-1.753
| to | =1.753
Critical Value
The Value of |t | with n-1 = 24 d.f is 1.711
We got |to| =1.753 & | t | =1.711
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Left Tail -Ha : ( P < -1.7532 ) = 0.04616
Hence Value of P0.05 > 0.04616,Here we Reject Ho

[ANS]
a.H0: U=8 , H1: U<8
b. to =-1.753, 24 d.f
c. 0.04616
d. Since p<a we reject the null hypothesis and accept the alternative. These data provide evidence that
New Yorkers sleep less than 8 hours a night on average

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