Two-Sample Inference

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Overview

  1. 10.1 Inference for Mean Difference—Dependent Samples
  2. 10.2 Inference for Two Independent Means
  3. 10.3 Inference for Two Independent Proportions
  4. 10.4 Inference for Two Independent Standard Deviations
  5. Chapter 10 Formulas and Vocabulary
  6. Chapter 10 Review Exercises
  7. Chapter 10 Quiz

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image Bank Loans

The Chapter 10 Case Study, Bank Loans examines a pair of large data sets, of 5000 observations each, of bank loan applicants: BankLoan_Approved and BankLoan_Denied (Source: Data Mining and Predictive Analytics,1 by Daniel Larose and Chantal Larose, John Wiley and Sons, 2015). The variables examined in these data sets include credit score, request amount, interest, debt-to-income ratio, and whether the loan application was approved or not.

  • In Section 10.2, we use the case study data for the following analysis:
    • We construct a two-sample confidence interval for the difference in mean credit score between loan applicants who were approved and those who were denied. We then use that confidence interval to conduct a series of hypothesis tests.
    • We conduct a pooled variance test for the difference in mean debt-to-income ratio between those approved and those denied the loan. Then we construct a pooled variance confidence interval for this difference.
    • In the Section 10.2 exercises, we examine whether a difference exists in the loan request amount between those approved and those denied the loan.
  • Finally, in the Section 10.3 exercises, we examine whether a difference exists in the proportion of applicants with credit scores of 700 or higher between those approved for and those denied the loan.

THE BIG PICTURE

Where we are coming from and where we are headed …

  • Thus far, our statistical inference has been limited to one population and one sample. In Chapter 8, we learned to construct confidence intervals, and in Chapter 9, we learned how to perform hypothesis tests, but all for a single population parameter.
  • Here, in Chapter 10, “Two-Sample Inference,” we perform inference on the differences in the parameters of two populations. For example, we may be interested in whether a difference exists in the population proportions of women and men who post personal information on the Internet.
  • In Chapter 11, we will turn to inference methods for categorical data, such as contingency tables.