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
*H*0. - 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
*H*0.

**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.