Some faculty believe that college students get less than 7 hours of sleep per night on average. A survey of 30 students found an average of 6.5 hours of sleep with a standard deviation of 1.8 hours. Are the faculty justified in their belief? Test this hypothesis at the 5% significance level.
State the Null Hypothesis, Alternative Hypothesis, and the p-value for the hypothesis test.
Then state your Decision (Reject H0 or Do Not Reject H0) and your Conclusion.
Solution :
=
7
=6.5
S =1.8
n = 30
This is the left tailed test .
The null and alternative hypothesis is ,
H0 : =
7
Ha :
< 7
Test statistic = t
= (
-
) / S /
n
= (6.5-7) / 1.8 /
30
= -1.521
Test statistic = t = -1.521
P-value =0.0695
= 0.05
P-value >
0.0695 > 0.05
Do Not Reject the null hypothesis .
There is not sufficient evidence to suggest that
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