Question

 

the night shift workeds in three of super bo’s specialty storws stock about 500 products in about 3 hours. how does this rate compare with fhe stocking done in the other 97 stores in the chain, which average about 496 products stocked in 3 hours? are the stockers at the specialty stores doing a “better than average” job?

specialty stores: size:3 average number of product stocked: 500 SD: 12.56

All stores: size:100 average number of product stocked:496 SD:22.13

Answer 1

Data:      

n1 = 3     

n2 = 97     

x1-bar = 500     

x2-bar = 496     

s1 = 12.56     

s2 = 22.13     

Hypotheses:     

Ho: μ1 ≤ μ2     

Ha: μ1 > μ2     

Decision Rule:     

α = 0.05     

Degrees of freedom = 3 + 97 - 2 = 98   

Critical t- score = 1.66055122    

Reject Ho if t > 1.66055122    

Test Statistic:     

Pooled SD, s = √[{(n1 - 1) s1^2 + (n2 - 1) s2^2} / (n1 + n2 - 2)] = √(((3 - 1) * 12.56^2 + (97 - 1) * 22.13^2)/(3 + 97 - 2)) = 21.9763903

SE = s * √{(1 /n1) + (1 /n2)} = 21.9763902998706 * √((1/3) + (1/97)) = 12.88278815

t = (x1-bar -x2-bar)/SE = (500 - 496)/12.882788147406 = 0.310491794

p- value = 0.37842319     

Decision (in terms of the hypotheses):   

Since 0.31049179 < 1.660551218 we fail to reject Ho

Conclusion (in terms of the problem):

There is no sufficient evidence that the speciality stores are doing any better