Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 444 gram setting. It is believed that the machine is underfilling the bags. A 20 bag sample had a mean of 443 grams with a standard deviation of 16. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled?

a. there is sufficient evidence that the bags are underfilled

b. there is not sufficient evidence that the bags are underfilled

Answer 1

Ho :   µ =   444                  
Ha :   µ <   444       (Left tail test)          
                          
Level of Significance ,    α =    0.10                  
sample std dev ,    s =    16.0000                  
Sample Size ,   n =    20                  
Sample Mean,    x̅ =   443.0000                  
                          
degree of freedom=   DF=n-1=   19                  
                          
Standard Error , SE = s/√n =   16   / √    20   =   3.5777      
t-test statistic= (x̅ - µ )/SE = (   443.000   -   444   ) /    3.578   =   -0.280
                          
  
p-Value   =   0.3914   [Excel formula =t.dist(t-stat,df) ]              
Decision:   p-value>α, Do not reject null hypothesis                       

conclusion:

b. there is not sufficient evidence that the bags are underfilled