6.6 - Confidence Intervals & Hypothesis Testing

Confidence intervals and hypothesis tests are similar in that they are both inferential methods that rely on an approximated sampling distribution. Confidence intervals use data from a sample to estimate a population parameter. Hypothesis tests, on the other hand, use data from a sample to test a specified hypothesis. Hypothesis testing requires that we have a hypothesized parameter. 

The simulation methods that we used to construct bootstrap distributions and randomization distributions were similar. The primary difference is that a bootstrap distribution is centered on the observed sample statistic while the randomization distribution is centered on the value in the null hypothesis. 

In Lesson 5 we learned that confidence intervals contained a range of reasonable estimates of the population parameter. All of the confidence intervals that we constructed were two-tailed. These two-tailed confidence intervals go hand-in-hand with the two-tailed hypothesis tests that you learned this week. The conclusion drawn from a two-tailed confidence interval is usually the same as the conclusion drawn from a two-tailed hypothesis. In other words, if the the 95% confidence interval contains the hypothesized parameter, then a hypothesis test at the 0.05 \(\alpha\) level should fail to reject the null hypothesis. If the 95% confidence interval does not contain the hypothesize parameter, then a hypothesis test at the 0.05 \(\alpha\) level should reject the null hypothesis.