PLEASE show all worksteps and fully explain An aspirin manuf

An aspirin manufacturer fills bottles 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 comparing 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]