In 2004 the average college student was 28 years old In 2006

In 2004, the average college student was 28 years old. In 2006, a quick sample of 64 college students found an average age of 28.5 with a standard deviation of 2.4 years. Has the average age increased? Perform a hypothesis test at the 5% significance level.

Hypotheses

Test Statistic

PValue

Conclusion

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   28  
Ha:    u   >   28   [ANSWER, HYPOTHESES]

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As we can see, this is a    right   tailed test.      
              
alpha =    0.05          
              
Getting the test statistic, as              
              
X = sample mean =    28.5          
uo = hypothesized mean =    28          
n = sample size =    64          
s = standard deviation =    2.4          
              
Thus, z = (X - uo) * sqrt(n) / s =    1.666666667 [ANSWER, TEST STATISTIC]

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Also, the p value is, by table/technology,              
              
p =    0.047790352   [ANSWER, P VALUE]

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As P < 0.05, we   REJECT THE NULL HYPOTHESIS.  

Thus, there is significant evidence that the mean age of college students increased.