It has been claimed that the mean age of all FHSU Virtual Co

It has been claimed that the mean age of all FHSU Virtual College statistics students is 28.65 years old. Using the age data collected from this summer\'s classes, test this hypothesis--that is does the collected data statistically support this claim or is the mean age likely different from 28.65 years old? Justify your answer through a formal hypothesis testing procedure with a 0.10 level of significance. Again, necessary claims, calculations, and values must be shown below and to the right. Give your proper/final conclusion below. (Hint: Since the population s.d. is not known, make sure to realize the need to use the t-distribution for testing purposes.)

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   28.65  
Ha:    u   =/   28.65  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    74          
tcrit =    +/-   1.665706893 [CRITICAL VALUES]      
              
Getting the test statistic, as              
              
X = sample mean =    30.77333333          
uo = hypothesized mean =    28.65          
n = sample size =    75          
s = standard deviation =    8.7341723          
              
Thus, t = (X - uo) * sqrt(n) / s =    2.105363329 [TEST STATISTIC]          
              
Also, the p value is              
              
p =    0.038653577   [P VALUE]      
              
Comparing |t| > 1.6657 (or, p < 0.10), we   REJECT THE NULL HYPOTHESIS.          
              
Thus, there is significant evidence that the mean age is different from 28.65 years old. [CONCLUSION]