PAGE O&M Statistics – Inferential Statistics: Hypothesis Testing Inferential Statistics Hypothesis testing Introduction In this week, we transition from confidence intervals and interval estimates to hypothesis testing, the basis for inferential statistics. Inferential statistics means using a sample to draw a conclusion about an entire population. A test of hypothesis is a procedure to determine whether sample data provide sufficient evidence to support a position about a population. This position or claim is called the alternative or research hypothesis. “It is a procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement” (Mason & Lind, pg. 336). This Week in Relation to the Course Hypothesis testing is at the heart of research. In this week, we examine and practice a procedure to perform tests of hypotheses comparing a sample mean to a population mean and a test of hypotheses comparing two sample means. The Five-Step Procedure for Hypothesis Testing (you need to show all 5 steps – these contain the same information you would find in a research paper – allows others to see how you arrived at your conclusion and provides a basis for subsequent research). Step 1 State the null hypothesis – equating the population parameter to a specification. The null hypothesis is always one of status quo or no difference. We call the null hypothesis H0 (H sub zero). It is the hypothesis that contains an equality. State the alternate hypothesis – The alternate is represented as H1 or HA (H sub one or H sub A). The alternate hypothesis is the exact opposite of the null hypothesis and represents the conclusion supported if the null is rejected. The alternate will not contain an equal sign of the population parameter. Most of the time, researchers construct tests of hypothesis with the anticipation that the null hypothesis will be rejected. Step 2 Select a level of significance (α) which will be used when finding critical value(s). The level you choose (alpha) indicates how confident we wish to be when making the decision. For example, a .05 alpha level means that we are 95% sure of the reliability of our findings, but there is still a 5% chance of being wrong (what is called the likelihood of committing a Type 1 error). The level of significance is set by the individual performing the test. Common significance levels are .01, .05, and .10. It is important to always state what the chosen level of significance is. Step 3 Identify the test statistic – this is the formula you use given the data in the scenario. Simply put, the test statistic may be a Z statistic, a t statistic, or some other distribution. Selection of the correct test statistic will depend on the nature of the data being tested (sample size, whether the population standard deviation is known, whether the data is known to be normally distributed). The sampling distribution of the test statistic is divided into t.