Question 982171: The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 10.0. As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for 8 full-time faculty for one week is shown in the table below. At α=0.10 can you reject the dean's claim? Complete parts (a) through (c) below.
Assume the population is normally distributed.
10.3,8.2,11.3,6.5,4.9,9.6,14.1,8.8
A. write the claim mathematically
B. What is the P value?
C. Decide whether to reject or fail to reject the null hypothesis.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! A) The claim is mu = 10.0
The claim is the null hypothesis. The alternate hypothesis is mu =/= 10.0, so we have a two tailed test.
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B)
Use a calculator to find that
xbar = 9.2125
s = 2.84677
Now compute the test statistic:
t = (xbar - mu)/(s/sqrt(n))
t = (9.2125- 10)/(2.84677/sqrt(8))
t = -0.78
Use either a table or a calculator to find that P(T < -0.78) = 0.23047 (the degrees of freedom equals n-1 = 8-1 = 7)
The p-value is therefore 2*0.23047 = 0.46094
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C)
The p-value 0.46094 is larger than alpha = 0.10. So we fail to reject the null. We "accept" the claim that the mean mu is 10.0. We don't have enough evidence to overturn it.
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