Question

The marketing manager of a firm that produces laundry products decides to test market a new laundry product in each of the firm's two sales regions. He wants to determine whether there will be a difference in mean sales per market per month between the two regions. A random sample of 12 supermarkets from Region 1 had mean sales of 84 with a standard deviation of 6.6. A random sample of 17 supermarkets from Region 2 had a mean sales of 78.3 with a standard deviation of 8.5. Does the test marketing reveal a difference in potential mean sales per market in Region 2? Let μ1 be the mean sales per market in Region 1 and μ2 be the mean sales per market in Region 2. Use a significance level of α=0.02 for the test. Assume that the population variances are not equal and that the two populations are normally distributed.

Step 1 of 4: State the null and alternative hypotheses for the test
Step 2 of 4: Compute the value of the t test statistic. Round your answer to three decimal places.
Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H0. Round your answer to three decimal places.
Step 4 of 4: State the test's conclusion

Answer 1

1)

H0: mu1 = mu2
Ha: mu1 not = mu2

2)

x1 = 84 , s1 = 6.6 , n1 =12
x2 = 78.3 , s2 = 8.5 , n2 = 17

t = (x1 -x20/sqrt(s1^2/n1+s2^2/n2)
= ( 84 - 78.3)/sqrt(6.6^2/12 + 8.5^2/17)
= 2.031

3)

   SE = sqrt[ (s12/n1) + (s22/n2) ]                  
   (s12/n1)   3.6300              
   (s22/n2)    4.2500              
   SE   2.8071              
                      
   DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] }                  
     [ (s12 / n1)2 / (n1 - 1) ]            1.198      
   [ (s22 / n2)2 / (n2 - 1) ]           1.13      
     (s12/n1 + s22/n2)2           62.09      
   DF =    27              

Reject H0 if t < -2.479 ot t > 2.479

4)

Fail to reject H0