Question

In: Statistics and Probability

During the investigation of an alleged unfair trade practice, the Federal Trade Commission takes a random...

During the investigation of an alleged unfair trade practice, the Federal Trade Commission takes a random sample of 50 “3-ounce” candy bars from a large shipment. If the mean and the standard deviation of their weights are, respectively, 2.92 ounces and 0.21 ounce, determine at the level of 0.01 significance whether the commission has grounds upon which to proceed against the manufacturer on the unfair practice of short-weight selling. State hypotheses, P-value, and conclusion.

Solutions

Expert Solution

Ho :   µ =   3                  
Ha :   µ <   3       (Left tail test)          
                          

Level of Significance ,    α =    0.010                  
sample std dev ,    s =    0.2100                  
Sample Size ,   n =    50                  
Sample Mean,    x̅ =   2.9200                  
                          
degree of freedom=   DF=n-1=   49                  
                          
Standard Error , SE = s/√n =   0.2100   / √    50   =   0.0297      
t-test statistic= (x̅ - µ )/SE = (   2.920   -   3   ) /    0.0297   =   -2.694
                          
critical t value, t* =        -2.405   [Excel formula =t.inv(α/no. of tails,df) ]              
                          
p-Value   =   0.0048   [Excel formula =t.dist(t-stat,df) ]              
Decision:   p-value<α, Reject null hypothesis                       
Conclusion: There is enough evidence to conclude that commission has grounds upon which to proceed against the manufacturer on the unfair practice of short-weight selling                    


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