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 72.4 with a standard deviation of 6.2. A random sample of 16 supermarkets from Region 2 had a mean sales of 78.3 with a standard deviation of 5.3. 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 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:
Reject Null Hypothesis or Fail to Reject Null Hypothesis

Answer #1

The statistical software output for this problem is :

Two sample T summary hypothesis test:

μ_{1} : Mean of Population 1

μ_{2} : Mean of Population 2

μ_{1} - μ_{2} : Difference between two means

H_{0} : μ_{1} - μ_{2} = 0

H_{A} : μ_{1} - μ_{2} ≠ 0

(without pooled variances)

**Hypothesis test results:**

Difference | Sample Diff. | Std. Err. | DF | T-Stat | P-value |
---|---|---|---|---|---|

μ_{1} -
μ_{2} |
-5.9 | 2.2268719 | 21.602919 | -2.6494564 | 0.0148 |

value of the t test statistic = -2.649

Critical value = 2.074

Reject the null hypothesis

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