The dean of a university estimates that the mean number of c

The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is10.0 As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for eight full-time faculty for one week is shown in the table below. At a=0.05, can you reject thedean\'s claim? Complete parts (a) through (d) below. Assume the population is normally distributed.

12.2, 8.1,11.3,6.2,4.8,10.1,14.2,8.1

Use technology to find the P-value.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   10  
Ha:    u   =/   10  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    7          
tcrit =    +/-   2.364624252      
              
Getting the test statistic, as              
              
X = sample mean =    9.375          
uo = hypothesized mean =    10          
n = sample size =    8          
s = standard deviation =    3.156738824          
              
Thus, t = (X - uo) * sqrt(n) / s =    -0.55999785          
              
Also, the p value is              
              
p =    0.592940967   [ANSWER, P VALUE]
              
Comparing t and tcrit (or, p and significance level), we   FAIL TO REJECT THE NULL HYPOTHESIS.          
Thus, there is no significant evidence that the mean classroom hours per week is not 10.0. [CONCLUSION]