Downtime in manufacturing is costly and can result in late d

Downtime in manufacturing is costly and can result in late deliveries, backlogs, failure to meet orders, and even loss of market share. Suppose a manufacturing plant has been averaging 23 minutes of downtime per day for the past several years, but during the past year, there has been a significant effort by both management and production workers to reduce downtime. In an effort to determine if downtime has been significantly reduced, company productivity researchers have randomly sampled 31 days over the past several months from company records and have recorded the daily downtimes shown below in minutes. Use these data and an alpha of .01 to test to determine if downtime has been significantly reduced. Assume that daily downtimes are normally distributed in the population.

19 22 17 19 32 24 16 18 27 17 24 19 23 27 28 19 17 18 26 22 19 15 18 25 23 19 26 21 16 21 24

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   23  
Ha:    u   <   23  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical z, as alpha =    0.01   ,      
alpha =    0.01          
zcrit =    -   2.326347874      
              
Getting the test statistic, as              
              
X = sample mean =    21          
uo = hypothesized mean =    23          
n = sample size =    31          
s = standard deviation =    4.86483984          
              
Thus, z = (X - uo) * sqrt(n) / s =    -2.288981568          
              
Also, the p value is              
              
p =    0.011040212          
              
As |z| < 2.326, and P > 0.02, we   FAIL TO REJECT THE NULL HYPOTHESIS.          
              
Thus, there is no significant evidence that the average downtime has been significantly reduced. [CONCLUSION]