The average cost of tuition room and board at small private

The average cost of tuition, room and board at small private liberal arts colleges is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745 with a standard deviation of $1,200. Let = 0.05. What is the p-value for this test? Choose the best option.

Solution

1. Formulating the null and alternative hypotheses,              
              
Ho:   u   =   8500  
Ha:    u   <   8500  
              
As we can see, this is a    1   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
              
zcrit =    1.644853627          
              
Getting the test statistic, as              
              
X = sample mean =    8745          
uo = hypothesized mean =    8500          
n = sample size =    350          
s = standard deviation =    1200          
              
Thus, z = (X - uo) * sqrt(n) / s =    3.819608582          
              
Also, the p value is              
              
p =    6.68318E-05 or 0.0000668, OR 0.0000, OPTION B.   [ANSWER]      

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Comparing z and zcrit (or, p and significance level), we   REJECT THE NULL HYPOTHESIS.