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 12 supermarkets from Region 1 had mean sales of 77.7 with a standard deviation of 8.7. A random sample of 17 supermarkets from Region 2 had a mean sales of 82.5 with a standard deviation of 6.8. 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=0.05 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 H0H0. Round your answer to three decimal places.

Step 4 of 4:

State the test's conclusion. (reject or fail to reject the null hypothesis)

Answer 1

1)

Ho :   µ1 - µ2 =   0
Ha :   µ1-µ2 ╪   0

2)

Level of Significance ,    α =    0.05          
                  
Sample #1   ---->   Region 1          
mean of sample 1,    x̅1=   77.70          
standard deviation of sample 1,   s1 =    8.7          
size of sample 1,    n1=   12          
                  
Sample #2   ---->   region 2          
mean of sample 2,    x̅2=   82.500          
standard deviation of sample 2,   s2 =    6.80          
size of sample 2,    n2=   17          
                  
difference in sample means = x̅1-x̅2 =    77.700   -   82.5000   =   -4.8000
                  
std error , SE =    √(s1²/n1+s2²/n2) =    3.0046          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -4.8000   /   3.0046   ) =   -1.598

3)

α=0.05

t-critical value , t* = ± 2.0930 (excel formula =t.inv(α/2,df)

Decision Rule:

Reject Ho, if test stat > 2.093 or test stat < -2.093

4)

since, test stat =-1.598 > -2.093 , do not reject Ho

answer: fail to reject the null hypothesis