A digital camcorder repair service has set a goal not to exc

A digital camcorder repair service has set a goal not to exceed an average of 5 working days from the time the unit is brought in to the time repairs are completed. A random sample of 12 repair records showed the following repair times (in days): 6, 6, 5, 7, 4, 6, 5, 11, 7, 6, 9, 7.

A) H₀: 5 days versus H₁: > 5 days. At = .05, choose the right option.

Reject H₀ if t_calc < 1.7960

Reject H₀ if t_calc >1.7960

B)Calculate the Test statistic. (round to 3 decimal places)

C) the null hypothesis should be rejected, true or false?

D)the average repair time is longer than 5 days, true or false?

E)At = .05 is the goal being met? yes or no?

Solution

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   5  
Ha:    u   >   5  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    11          
tcrit =    +   1.795884819      

Thus, we

REJECT HO IF TCALC > 1.7960. [ANSWER]

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b)

              
Getting the test statistic, as              
              
X = sample mean =    6.583333333          
uo = hypothesized mean =    5          
n = sample size =    12          
s = standard deviation =    1.880924982          
              
Thus, t = (X - uo) * sqrt(n) / s =    2.916 [ANSWER]

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c)

As t > 1.7960, we REJECT HO. [TRUE]

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d)          
              
Thus, the avergae repair time is longer than 5 days. [TRUE]

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e)

From d, NO. [ANSWER]

The goal is not met, as the goal is to be less than 5 days.