Hypothesis Testing Question You would like to determine if t

You would like to determine if the average accounting audit delay for a public company exceeds 90 days. Suppose a random sample of 100 public companies has an average delay of 96.6 days and a standard deviation of 32.83 days. What is the appropriate null and alternative hypothesis to test that the average audit delay exceeds 90 days? Test the hypothesis using a = 0.05. Explicitly show the critical value(s), rejection region and how you compute the test statistic. Explicitly state whether or not you reject the null hypothesis and why. Compute the p-value for the test statistic and discuss how you would use this value to decide whether or not to reject the null hypothesis. Do you reach the same conclusion you reached in part b?

Solution

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   90  
Ha:    u   >   90   [ANSWER]

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B)
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha =    0.05          
zcrit =    +   1.644853627   [ANSWER, CRITICAL VALUE]

Thus, we reject Ho if z > 1.64485. [ANSWER, REJECTION REGION]  
              
Getting the test statistic, as              
              
X = sample mean =    96.6          
uo = hypothesized mean =    90          
n = sample size =    100          
s = standard deviation =    32.83          
              
Thus, z = (X - uo) * sqrt(n) / s =    2.010356381   [ANSWER, TEST STATISTIC]
              
Comparing z > zcrit, we   REJECT THE NULL HYPOTHESIS.   [CONCLUSION]

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C)

Also, the right tailed p value is, by using technology,
      
p =    0.022196742

As p < 0.05, we REJECT the null hypothesis (still).

Yes, this is the same as part B.