## 3. Using Confidence Intervals to Test Hypotheses

This is probably the easiest (and most understandable) method for testing a claim about a population proportion, as long as our null hypothesis contains the condition of not equal. Recall from sub-competency 8 that a confidence interval represents a range of values that we believe, with level C confidence, contains or captures the true population mean or proportion. We can use this interval to test the null hypothesis. The key to understanding this is to realize that a level C = (1 – α) ⋅ 100% confidence interval gives us the same results as a hypothesis test using a level of significance α. For example, a 95% confidence interval can be used in place of a hypothesis test using a significance level α = 0.05 = 5%.

To use a confidence interval, simply make the following observations:

• If our confidence interval contains the value claimed by the null hypothesis, then our sample result is close enough to the claimed value, and we therefore do not reject H0.
• If our confidence interval does not contain the value claimed by the null hypothesis, then our sample result is different enough from the claimed value, and we therefore reject H0.

A final note: The two main assumptions that we must have in order for the statistical calculations of hypothesis testing to be valid are (1) the sample data must be obtained through some random procedure, and (2) the sample data should (roughly) form a normal distribution with no strong skewness and no huge outliers. To check the (rough) normalcy of the data, you can simply create a stem-and-leaf plot and look at the overall pattern.