# 9.3 - Lesson 9 Summary

9.3 - Lesson 9 Summary## Objectives

Upon successful completion of this lesson, you should be able to:

- Identify situations in which the z or t distribution may be used to approximate a sampling distribution
- Construct a confidence interval to estimate the difference in two population proportions and two population means using Minitab Express given summary or raw data
- Conduct a hypothesis test for two proportions and two means using Minitab Express given summary or raw data

Confidence Interval | Test Statistic | |
---|---|---|

Two Independent Proportions At least 10 successes and 10 failures in both samples. |
\((\widehat{p}_1-\widehat{p}_2) \pm z^\ast {\sqrt{\frac{\widehat{p}_1 (1-\widehat{p}_1)}{n_1}+\frac{\widehat{p}_2 (1-\widehat{p}_2)}{n_2}}}\) | \(z=\frac{\widehat{p}_1-\widehat{p}_2}{\sqrt{\widehat{p}(1-\widehat{p})\left ( \frac{1}{n_1}+\frac{1}{n_2} \right )}}\) |

Two Independent Means Both sample size are at least 30 OR populations are normally distributed. |
\((\bar{x}_1-\bar{x}_2) \pm t^\ast{ \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}\) \(Estimated \;df = smallest\; n - 1\) |
\(t=\frac{\bar{x}_1-\bar{x}_2}{ \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}\) \(Estimated \;df = smallest\; n - 1\) |