An aspirin manufacturer fills bottle by weight rather than b

An aspirin manufacturer fills bottle by weight rather than by count. Since each bottle should contain 100 tablets, the average weight per tablet should be 5 grains. Each of 100 tablets taken from a very large lot is weighed, resulting in a sample average weight per tablet of 4.87 grains and a sample standard deviation of .35 grain. Does this information provide strong evidence for concluding that the company is not filling its bottles as advertised? Test the appropriate hypotheses using alpha = .01 by first computing the p-value and then computing it to the specified significance level.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   5  
Ha:    u   =/   5  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical z, as alpha =    0.01   ,      
alpha/2 =    0.005          
zcrit =    +/-   2.575829304      
              
Getting the test statistic, as              
              
X = sample mean =    4.87          
uo = hypothesized mean =    5          
n = sample size =    100          
s = standard deviation =    0.35          
              
Thus, z = (X - uo) * sqrt(n) / s =    -3.714285714          
              
Also, the p value is              
              
p =    0.000203778          
              
As |z| > 2.576, and P < 0.01, we   REJECT THE NULL HYPOTHESIS.          

Thus, there is significant evidnece that the company is not filling its bottles as advertised, the mean is not 5 grains at 0.01 level. [CONCLUSION]