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The mean length of a candy bar is 43 millimeters. There is concern that the sett

ID: 3124523 • Letter: T

Question

The mean length of a candy bar is 43 millimeters. There is concern that the settings of the machine cutting the bars have changed. Test the claim at the 0.02 level that there has been no change in the mean length. The alternate hypothesis is that there has been a change. Twelve bars (n = 12) were selected at random and their lengths recorded. The mean of the sample is 41.5 and the standard deviation is 1.784. Has there been a statistically significant change in the mean length of the bars?

The mean length of a candy bar is 43 millimeters. There is concern that the settings of the machine cutting the bars have changed. Test the claim at the 0.02 level that there has been no change in the mean length. The alternate hypothesis is that there has been a change. Twelve bars (n = 12) were selected at random and their lengths recorded. The mean of the sample is 41.5 and the standard deviation is 1.784. Has there been a statistically significant change in the mean length of the bars?

Explanation / Answer

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   43  
Ha:    u   =/   43  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    11          
tcrit =    +/-   2.718079184      
              
Getting the test statistic, as              
              
X = sample mean =    41.5          
uo = hypothesized mean =    43          
n = sample size =    12          
s = standard deviation =    1.784          
              
Thus, t = (X - uo) * sqrt(n) / s =    -2.912641493          
              
Also, the p value is              
              
p =    0.014122142          
              
As |t| > 2,718, and P < 0.02, we   REJECT THE NULL HYPOTHESIS.          

Hence, YES, THERE HAS BEEN A CHANGE IN THE MEAN LENGTH OF THE BARS. [CONCLUSION]

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