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.

Answer 1

the null and alternative hypotheses for the test is

Ho: There will be no difference in mean sales per market per month between the two regions

H1: There will be a difference in mean sales per market per month between the two regions

i.e Ho:

H1:

here a test of statistics is

where ,

,

,

hence the value of t is given as

t = 2.031

now the t critical value ( t-table) =

we can get t table value from table

= t-table = 2.474

Decision about the null hypothesis :

t = 2.031 < 2.474 = t -table

hence null hypothesis His not rejected. Therefore, there is not enough evidence to claim that the population mean μ1​ is different thanμ2​, at the 0.02 significance level.

Conclusion :  

There will be no difference in mean sales per market per month between the two regions