- Describe how a two-sample confidence interval is related to a hypothesis test for the difference between two dependent population means
Inferences with Confidence Intervals
A confidence interval provides a range of population values with which a sample statistic is consistent at a given confidence level. In many cases, confidence intervals can also be used to either reject or not reject the null hypothesis, and therefore perform the same function as the typical hypothesis test. A [latex]95\%[/latex] confidence interval would be used to test the null hypothesis at the [latex]5\%[/latex] significance level. A [latex]99\%[/latex] confidence interval would be used to test the null hypothesis at the [latex]1\%[/latex] significance level.
Let’s find the [latex]95\%[/latex] confidence interval and see if we can answer the research question: “Does a driver’s reaction times (in milliseconds) differ when they are using a cell phone as opposed to when they are not using a cell phone?”
Step 1: Click on the tab Two Dependent Samples.
Step 2: In the “Dataset” drop-down menu, choose “Reaction Times (Paired Experiment).”
Step 3: In the left column, go to the drop-down menu for “Type of Inference” and select “Confidence Interval”.
Step 4: Use the slider to select the correct “Confidence Level”.
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- If a confidence interval contains the hypothesized parameter, a hypothesis test at the [latex]0.05[/latex] level will almost always fail to reject the null hypothesis.
- If the [latex]95\%[/latex] confidence interval does not contain the hypothesized parameter, a hypothesis test at the [latex]0.05[/latex] level will almost always reject the null hypothesis.