Question

Managerial problem

Option A: 25-cent off coupon Option B: 50-cent off coupon
Prior to making the decision as to which coupon to use in the marketing program, manager wants a

marketing research to be conducted.

Experiment

A new product was tested in JC with a 25-cent off coupon and another with a 50-cent off coupon. A sample of 100 people was contacted for each coupon. A total of 30 percent of those contacted with 25-cent off coupon had tried the new product, whereas 40 percent of those contacted with 50-cent off coupon had tried it, a 10 – percent difference.

Answer the following in detail.

1. What statistical test (difference analysis) you suggest for the above problem?

2. What should the null hypothesis be?

The probability of obtaining this result under the null hypothesis, namely, that the trial level with 50-cent off coupon was 10 percent higher than that with 25-cent off coupon, was determined to be 0.04.

3. Is the result significant at the (two-tailed) 0.05 level?

4. Is the result significant at the (two-tailed) 0.10 level?

5. Do you suggest manager that a 50-cent coupon be used?

Answer 1

A sample of 100 people was contacted for each coupon.

p1 = Proportion of people who tried the new product with 25-cent off coupon = 30%

p2 = Proportion of people who tried the new product with 50-cent off coupon = 40%

We will use Z-test for two population proportions (p1​ and p2​) to analyze the problem.

The null hypothesis would be Ho: p1 = p2

The probability of obtaining this result under the null hypothesis, namely, that the trial level with 50-cent off coupon was 10 percent higher than that with 25-cent off coupon, was determined to be 0.04.

The p-value is 0.04.

Yes, the result is significant at the (two-tailed) 0.05 level because the p-value is less than 0.05.

Yes, the result is significant at the (two-tailed) 0.10 level because the p-value is less than 0.05.

Yes, we will suggest the manager that the 50-cent coupons be used as our hypothesis test supports our claims.