The recommended number of hours of sleep per night is 8 hour

The recommended number of hours of sleep per night is 8 hours, but everybody \"knows\" that the average college student sleeps less than 7 hours. The number of hours slept last night by 10 randomly selected college students is listed below. Complete the following hypothesis test: H_o: = 7, H_a: < 7, = 0.05.

(a) Find t. (Give your answer correct to two decimal places.)

(ii) Find the p-value. (Give your answer correct to four decimal places.)

state decision

Solution

Set Up Hypothesis
Null Hypothesis H0: U<7
Alternate Hypothesis H1: U>7
Test Statistic
Population Mean(U)=7
Sample X(Mean)=7.09
Standard Deviation(S.D)=0.8736
Number (n)=10
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =7.09-7/(0.8736/Sqrt(9))
to =0.326
| to | =0.326
Critical Value
The Value of |t | with n-1 = 9 d.f is 1.833
We got |to| =0.326 & | t | =1.833
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Right Tail - Ha : ( P > 0.3258 ) = 0.37602
Hence Value of P0.05 < 0.37602,Here We Do not Reject Ho