2 A word processing center claims that it provides an averag

2. A word processing center claims that it provides an average turnaround time of 3.2 days or less. In order to test this claim a sample of 16 jobs was taken. The sample mean turnaround time was equal to 3.4 days and the sample standard deviation was equal to 1.9 days. Assuming a normal population distribution, test the null hypothesis that the true mean is 3.2 days against the alternative that it is greater, at the 5 percent significance level.

Step 1: Write the null & alternative hypotheses and Write the significance level of the test

Step 2: write the appropriate test-statistic and Find the calculated value of the test-statistic or plug & chug.

Step 3:   Find and write the critical value of the test

Step 4: Write your decision about this test.

Solution

1.

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   3.2  
Ha:    u   >   3.2  
              
As we can see, this is a    right   tailed test, at 0.05 level.

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2.  

We use t distribution as n is small, 16 < 30.              
              
Getting the test statistic, as              
              
X = sample mean =    3.4          
uo = hypothesized mean =    3.2          
n = sample size =    16          
s = standard deviation =    1.9          
              
Thus, t = (X - uo) * sqrt(n) / s =    0.421052632 [ANSWER]          

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3.

Thus, getting the critical t, by table/technology,              

df = n - 1 =    15          

tcrit =    +   1.753050356   [ANSWER]

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4.

As |t| < 1.753, we   FAIL TO REJECT THE NULL HYPOTHESIS.  

Thus, there is no significant evidence that the average turnaround time is more than 3.2 days. [ANSWER]