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Chapter 10: Problem 4

Credit cards and incentives A bank wants to know which of two incentive plans will most increase the use of its credit cards. It offers each incentive to a group of current credit card customers, determined at random, and compares the amount charged during the following six months. (a) Is this a problem about comparing means or comparing proportions? Explain. (b) What type of study design is being used to produce data?

Short Answer

Expert verified
(a) Comparing means; (b) Experimental design.

Step by step solution

01

Identify the Data Type Being Compared

The bank is interested in seeing which incentive plan leads to a higher amount charged on the credit cards. Since these amounts are numerical values, the problem is about comparing the means of these amounts across different groups.
02

Determine the Nature of the Study

The bank assigns two different incentive plans to two random groups of its current credit card customers to compare the outcome (credit card usage). This random assignment of treatments to subjects indicates that the study uses an experimental design.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Comparing Means
When discussing comparing means, we're focusing on analyzing average values across different groups. In this scenario, the bank wants to determine which of two incentive plans leads to a higher average credit card usage among its customers over a six-month period.

Here's why comparing means is important:
  • Understanding Trends: By comparing the averages, we can identify which incentive plan, on average, leads to more credit card spending.
  • Insights and Decisions: If one plan results in a significantly higher average expenditure, the bank might decide to implement it more broadly to increase overall revenue.
In comparing means, it鈥檚 crucial to ensure that the data is normally distributed and that sample sizes are large enough to draw meaningful conclusions. This involves calculating the average amount spent under each plan and using statistical tests to determine if the differences observed are statistically significant.
Random Assignment
Random assignment is a crucial component of experimental design. It involves assigning participants to different groups entirely by chance, ensuring that each person has an equal probability of receiving any of the available treatments (in this case, the incentive plans).

Here's why random assignment is essential in experiments:
  • Eliminates Bias: By randomly assigning subjects to groups, we prevent any bias that might occur if assignment was done based on characteristics like spending history or customer loyalty.
  • Creates Comparable Groups: It helps create groups that are similar in all respects at the start of the experiment, meaning any differences observed in outcomes can be attributed to the incentive plans.
  • Increase Validity: Random assignment strengthens the internal validity of the study, providing more reliable evidence on the causal effects of the incentive plans.
Random assignment helps ensure that the conclusions drawn from the experiment are valid and can serve as a reliable basis for decision-making.
Incentives Study
An incentives study focuses on understanding how various incentives can influence behavior. In the bank's experiment, they are investigating how different incentive plans affect credit card usage.

Key aspects of an incentives study include:
  • Testing Incentives: Different types of incentives might be tested, such as cashback rewards or travel points, to see which encourages more spending.
  • Behavioral Impact: Researchers aim to see if these incentives lead to a measurable change in behavior, such as increased spending on credit cards.
  • Long-term vs. Short-term Effects: The study would typically look at not only the immediate impact of the incentives but also if these effects sustain over time.
The ultimate objective of an incentives study is to provide actionable insights that can inform marketing strategies and optimize customer engagement. Such studies often involve rigorous data collection and analysis to ensure the findings are robust and actionable.

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Most popular questions from this chapter

Who talks more鈥攎en or women? Researchers equipped random samples of 56 male and 56 female students from a large university with a small device that secretly records sound for a random 30 seconds during each 12.5-minute period over two days. Then they counted the number of words spoken by each subject during each recording period and, from this, estimated how many words per day each subject speaks. The female estimates had a mean of 16,177 words per day with a standard deviation of 7520 words per day. For the male estimates, the mean was 16,569 and the standard deviation was 9108. (a) Do these data provide convincing evidence of a difference in the average number of words spoken in a day by male and female students at this university? Carry out an appropriate test to support your answer. (b) Interpret the P-value from part (a) in the context of this study.

Web business You want to compare the daily sales for two different designs of Web pages for your Internet business. You assign the next 60 days to either Design A or Design B, 30 days to each. (a) Describe how you would assign the days for Design A and Design B using the partial line of random digits provided below. Then use your plan to select the first three days for using Design A. Show your method clearly on your paper. $$24005 \qquad 52114 \qquad 26224 \qquad 39078$$ (b) Would you use a one-sided or a two-sided significance test for this problem? Explain your choice. Then set up appropriate hypotheses. (c) If you plan to use Table B to calculate the P-value, what are the degrees of freedom? (d) The t statistic for comparing the mean sales is 2.06. Using Table B, what P-value would you report? What would you conclude?

Exercises 33 and 34 refer to the following setting. Thirty randomly selected seniors at Council High School were asked to report the age (in years) and mileage of their main vehicles. Here is a scatterplot of the data: We used Minitab to perform a least-squares regression analysis for these data. Part of the computer output from this regression is shown below. Predictor \(\quad\) coef \(\quad\) stdev \(\quad\) t-ratio \(\quad \mathrm{P}\) Constant \(-13832 \qquad 8773 \qquad-1.58 \qquad 0.126\) Age \(\quad 14954 \qquad 1546 \qquad 9.67 \quad 0.000\) \(s=22723 \qquad R-s q=77.08 \qquad R-s q(a d j)=76.18\) Drive my car (3.2) (a) What is the equation of the least-squares regression line? Be sure to define any symbols you use. (b) Interpret the slope of the least-squares line in the context of this problem. (c) One student reported that her 10-year-old car had 110,000 miles on it. Find the residual for this data value. Show your work.

Binge drinking Who is more likely to binge drink鈥攎ale or female college students? The Harvard School of Public Health surveys random samples of male and female undergraduates at four-year colleges and universities about whether they have engaged in binge drinking. (a) Is this a problem about comparing means or comparing proportions? Explain. (b) What type of study design is being used to produce data?

What鈥檚 wrong? A driving school wants to find out which of its two instructors is more effective at preparing students to pass the state鈥檚 driver鈥檚 license exam. An incoming class of 100 students is randomly assigned to two groups, each of size 50. One group is taught by Instructor A; the other is taught by Instructor B. At the end of the course, 30 of Instructor A鈥檚 students and 22 of Instructor B鈥檚 students pass the state exam. Do these results give convincing evidence that Instructor A is more effective? Min Jae carried out the significance test shown below to answer this question. Unfortunately, he made some mistakes along the way. Identify as many mistakes as you can, and tell how to correct each one. State: I want to perform a test of $$H_{0} : p_{1}-p_{2}=0$$ $$H_{a} : p_{1}-p_{2}>0$$ where \(p_{1}=\) the proportion of Instructor A's students that passed the state exam and \(p_{2}=\) the proportion of Instructor B's students that passed the state exam. Since no significance level was stated, I'll use \(\sigma=0.05\) Plan: If conditions are met, I'll do a two-sample \(z\) test for comparing two proportions. \(\bullet\) Random The data came from two random samples of 50 students. \(\bullet\) Normal The counts of successes and failures in the two groups - \(30,20,22\) , and \(28-\) are all at least \(10 .\) \(\bullet\) Independent There are at least 1000 students who take this driving school's class. Do: From the data, \(\hat{p}_{1}=\frac{20}{50}=0.40\) and \(\hat{p}_{2}=\frac{30}{50}=0.60 .\) So the pooled proportion of successes is $$\hat{p}_{C}=\frac{22+30}{50+50}=0.52$$ \(\bullet\) Test statistic $$z=\frac{(0.40-0.60)-0}{\sqrt{\frac{0.52(0.48)}{100}+\frac{0.52(0.48)}{100}}}=-2.83$$ Conclude: The P-value, \(0.9977,\) is greater than \(\alpha=\) \(0.05,\) so we fail to reject the null hypothesis. There is not convincing evidence that Instructor A's pass rate is higher than Instructor B's.
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