Chapter 12

# Chapter 12 - MSIT 3000 Chapter 12 Comparing Two Groups Do...

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MSIT 3000 Chapter 12 Comparing Two Groups Do customers spend more using their credit card if they are given an incentive such as “double miles” or “double coupons” toward flights, hotel stays, or store purchases? To answer questions such as this, credit card issuers often perform experiments on a sample of customers, making them an offer of an incentive, while other customers receive no offer. By comparing the performance of the two offers on the sample, they can decide whether the new offer would provide enough potential profit if they were to “roll it out” and offer it to their entire customer base. 172

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MSIT 3000 Section 12.1 Comparing Two Means The natural display for comparing the means of two groups is side-by-side boxplots. For the credit card promotion, the company judges performance by comparing the mean spend lift (the change in spending from before receiving the promotion to after receiving it) for the two samples. If the difference in spend lift between the group that received the promotion and the group that didn’t is large enough, this will be considered evidence that the promotion worked. What do you think from the boxplots? What IS a “large enough” difference? 173
MSIT 3000 Section 12.2 The Two-Sample t-Test To determine what is “large enough,” we need a statistical inference procedure. The statistic of interest is the difference in the observed means of the offer and no offer groups: y 0 y n . What we’d really like to know is the difference of the means in the population: μ 0 μ n . For a hypothesis test for the difference of the means, the hypothesized difference between the two groups is zero. Independent Groups Assumption: To use the two-sample t methods, the two groups we are comparing must be independent of each other. No statistical test can verify that the groups are independent. You have to think about how the data were collected. The test can be called a two-sample t-test, or a hypothesis test for two independent means. 174

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Ex: Consumers increasingly make food purchases based on nutritional values. In the July 2007 issue, Consumer Reports compared the calorie content of meat and beef hot dogs. The researchers purchased samples of several different brands. The meat hot dogs averaged 111.7 calories compared to 135.4 for the beef hot dogs. A test of the null hypothesis that there’s no difference in mean calorie content yields a p-value of 0.024. Let α = 0.05. a. State the null and alternative hypotheses.
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## This note was uploaded on 01/10/2012 for the course MIST 3000 taught by Professor Kim during the Fall '11 term at UGA.

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Chapter 12 - MSIT 3000 Chapter 12 Comparing Two Groups Do...

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