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:
μ₁ : Mean of Population 1
μ₂ : Mean of Population 2
μ₁ - μ₂ : Difference between two means
H₀ : μ₁ - μ₂ = 0
H_A : μ₁ - μ₂ ≠ 0
(without pooled variances)

Hypothesis test results:

Difference	Sample Diff.	Std. Err.	DF	T-Stat	P-value
μ1 - μ2	-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