The depot is using a standard of 635 hours for a particular

The depot is using a standard of 635 hours for a particular modification effort. You are to review the standard and determine whether it should be revised. After sampling 20 of these modifications you calculate a mean of 665 hours and a standard deviation of 45 hours. We are concerned that the hours might be higher or lower than the 635 hour standard. Test the standard at the .05 level of significance. Select the correct answer out of each pair of choices. (Carry intermediate calculations to three decimal places.) The tp is 2.093 The tp is 1.729 The tc is 2.981 The tc is 13.333 We would reject the null hypothesis We would fail to reject the null hypothesis We would recommend using the existing standard. We would recommend revising the standard.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   635  
Ha:    u   >   635  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    19          
tcrit =    +   1.729132812      
              
Getting the test statistic, as              
              
X = sample mean =    665          
uo = hypothesized mean =    635          
n = sample size =    20          
s = standard deviation =    45          
              
Thus, t = (X - uo) * sqrt(n) / s =    2.98142397          
              
Hence,

t = 2.981, tcrit = 1.729 [ANSWER]

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As t > 1.729, WE REJECT THE NULL HYPOTHESIS.

WE WOULD RECOMMEND REVISING THE STANDARD.