4.8 - Lesson 4 Summary

Objectives

Upon completion of this lesson, you will be able to:

  • Construct and interpret sampling distributions using StatKey
  • Explain the general form of a confidence interval
  • Interpret a confidence interval
  • Explain the process of bootstrapping
  • Construct bootstrap confidence intervals using the standard error method
  • Construct bootstrap confidence intervals using the percentile method in StatKey
  • Construct bootstrap confidence intervals using Minitab Express
  • Describe how sample size impacts a confidence interval

As you work through the textbook reading and assignments this week you may want to have a copy of the table below. One of the biggest challenges students often face in this lesson is being able to select the correct procedure.  Whether you're constructing a confidence interval for a single mean, single proportion, single proportion, etc., depends on what type of variable or variables you are working with. You may want to return to the earlier lessons to review categorical and quantitative variables.

  Population Parameter Sample Statistic
Single mean \(\mu\) \(\overline x\)
Difference in two independent means \(\mu_1 - \mu_2\) \(\overline x_1 - \overline x_2\)
Single proportion \(p\) \(\widehat p\)
Difference in two proportions \(p_1 - p_2\) \(\widehat p_1 - \widehat p_2\)
Correlation \(\rho\) \(r\)
Slope (simple linear regression) \(\beta\) \(b\)

Note: In this lesson we also learned how to construct a confidence interval for the difference in paired means. We use this procedure when each case (i.e., participant) has two observations and we want to estimate the average difference. In this case, the population parameter is \(\mu_d\) and the observed sample statistic is \(\overline x_d\). This is treated as a single sample mean test where the variable that we're working with is the difference.