**Hamilton Marketing Service Case**

**Compute a sample proportion of the responses for the two coupon options under consideration.**

According to the case, the sample proportion of pricing option will be 1 on 40 dollars it will be 6/80 = 0.2 which means 20% . Now if the sample proportion of pricing is 2 on 30 dollars then it will be 14/ 80 = 0.175 which means the answer is 17.5%

**Develop a 95% confidence interval for the difference between the proportions of responses between the two options.**

According to the evaluation performed the pricing option 1 with 40 dollar rate shows that there is 95% chance that the customers are confident about it and will going to prefer the 40 dollar price option and proportion, however, will remain 11.2% to 28.7%. Now if we talk about the pricing option 2 with 30 dollar rate shows that there is 95% chance the customer will be confident to purchase 30 dollar price option, and proportion in this will be 9.2% to 25.8%.

**Use the confidence interval developed in question 2 to draw a conclusion regarding whether or not there is any statistical evidence that there is a difference in response rate between two coupon options**.

When we thoroughly analyzed the data, it is not completely clear which pricing option is better for the Pet grooming company. Because both confidence intervals overlie each other and data regarding this is incomplete that’s why it is not possible to tell which is better.

**Determine whether or not there is a difference between the two coupon options regarding revenue generated**.

As there is not enough information but we can estimate revenue generation. As we can see 40 dollar coupon have a large proportion of response, so it means the revenue generation in 40 dollar coupon is low. However, the 30 dollar coupon response is less, but it will generate a high level of revenue. If the discount is high revenue generation is less, and if the discount is low, it means revenue generation is high.

**Identify any other issues or factors that should be considered in deciding which coupon option to use.**

As there is not enough information identifying different factors is a difficult task. The factor that can be identified is the amount of discount. It is better to select that option in which discount and customer convenience are high. The expiration date should also be considered so that customer could avail the benefit before expiration.

**Develop a short report summarizing your analysis and conclusions**

If we summarize the above calculation and analysis, we will come to know that customer response on that price option in which they feel they have more benefit. Price 1 option has the higher response because it is providing more benefit then the price option 2. Other factors are not clearly analyzed due to the short amount of information available.

**To determine which hypothesis test procedure needs to be used**

The t-test should be the optimum choice because it will determine the result by two independent samples of two population means. If you want to check whether the variance is equal or not, then two-sample variance test can be applied.

**Indicate the appropriate test that should be used to determine if a difference exists**T-test is the test that can be used if a difference is present. But if a difference is not present then pooled T-test can be used.

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