A. State the null and alternative hypotheses for the test. B. Compute the value

Question

A. State the null and alternative hypotheses for the test.

B. Compute the value of the t-test statistic. Round to 3 decimals.

C.Determine the decision rule for rejecting the null hypothesis H0. Round to 3 decimals.

D. Determine the decision rule for rejecting the null hypothesis. Round the numerical portion of your answer to two decimal places. [Reject H0 if (t or absolute value of t) is (< or >)   (value) ]

State the test's conclusion: Reject or Fail to Reject Null Hypothesis

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 77.8 with a standard deviation of 5.1. A random sample of 16 supermarkets from Region 2 had a mean sales of 83.8 with a standard deviation of 5.9. Does the test marketing reveal a difference in potential mean sales per market in Region 2? Let be the mean sales per market in Region 1 and 2 be the mean sales per market in Region 2. Use a significance level of = 0.05 for the test. Assume that the population variances are not equal and that the two populations are normally distributed the 6 su sales levl 005 egion 22 armt

Explanation / Answer

Result:

A. State the null and alternative hypotheses for the test.

Ho: µ1 = µ2       H1: µ1 µ2

B. Compute the value of the t-test statistic. Round to 3 decimals.

Population 1 Sample

Sample Size

12

Sample Mean

77.8

Sample Standard Deviation

5.1000

Population 2 Sample

Sample Size

16

Sample Mean

83.8

Sample Standard Deviation

5.9000

Intermediate Calculations

Standard Error

2.0840

Difference in Sample Means

-6.0000

Separate-Variance t Test Statistic

-2.8791

Test statistic = -2.879

C.Determine the decision rule for rejecting the null hypothesis H0. Round to 3 decimals.

since assumong population variances are not equal,

Table value of t with 11 DF at 0.05 level = 2.201

Reject Ho if calculated t < -2.201 or t > 2.201

D. Determine the decision rule for rejecting the null hypothesis. Round the numerical portion of your answer to two decimal places.

Reject H0 if (t or absolute value of t) is > 2.20

State the test's conclusion: Reject Null Hypothesis

Population 1 Sample

Sample Size

12

Sample Mean

77.8

Sample Standard Deviation

5.1000

Population 2 Sample

Sample Size

16

Sample Mean

83.8

Sample Standard Deviation

5.9000

Intermediate Calculations

Standard Error

2.0840

Difference in Sample Means

-6.0000

Separate-Variance t Test Statistic

-2.8791

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