A quality control experiment is to be done on a machine that fills tubes with to

Question

A quality control experiment is to be done on a machine that fills tubes with toothpaste. Its specifications require that it fills tubes with 4.7 oz.A random sample of 40 tubes filled by the machine is taken and each tube is weighted. The resulting data are below , with the weight of the tube already having been subtracted from each. Perform a hypothesis test at the 90% confidence level to determine if the machine is performing according to specification

4.66 4.61 4.71 4.63 4.70 4.62 4.63 4.61 4.70 4.56

4.60 4.66 4.68 4.57 4.67 4.72 4.67 4.64 4.66 4.75

4.69 4.64 4.67 4.65 4.69 4.65 4.75 4.53 4.57 4.74

4.68 4.67 4.66 4.68 4.64 4.65 4.64 4.80 4.71 4.69

Explanation / Answer

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   4.7  
Ha:    u   =/   4.7  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical z, as alpha =    0.1   ,      
alpha/2 =    0.05          
zcrit =    +/-   1.644853627      
              
Getting the test statistic, as              
              
X = sample mean =    4.661          
uo = hypothesized mean =    4.7          
n = sample size =    40          
s = standard deviation =    0.054103415          
              
Thus, z = (X - uo) * sqrt(n) / s =    -4.559003506          
              
Also, the p value is              
              
p =    5.13969E-06          
              
As |z| > 1.645, and P < 0.10, we   REJECT THE NULL HYPOTHESIS.      

Hence, there is significant evidence at 0.10 level that the machine is performing according to specification, that is, the mean is not 4.7 oz.   [CONCLUSION]

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