1 © Lecture note 3 Hypothesis Testing MAKE HYPOTHESIS ©

2 Hypothesis Testing Statistical inference: making decisions about a population based on observations of a sample. Scientific hypothesis: a testable statement about nature that requires verification An informed guess about a phenomena.

3 Statistical Hypotheses A statement about one or more parameters of a population distribution that requires verification The population mean is greater than 115. The population mean is less than or equal to 115 These statements are mutually exclusive. If one is true, the other must be false.

4 Null Hypothesis Alternative Hypothesis Only the null hypothesis is actually tested. The process of choosing between the null and alternative hypotheses is called hypothesis testing.

5 More Hypothesis Testing Usually, the null hypothesis is contrary to what we believe to be true about the population. Usually, the alternative hypothesis describes the situation we believe to be true. ***If the obtained statistic is unlikely to be true, we reject the null hypothesis.

6 Rejection of the Null Hypothesis Only means that the alternative hypothesis is probably true. It’s tenable, that is, justifiable, or there is evidence for it. Deciding to reject is based on 1. Test statistic (random sample) 2. Hypothesis testing conventions 3. Decision rule

7 Steps In Hypothesis Testing 1. State the Hypothesis* 2. Specify the test statistic 3. Specify the size of n 4. Set the criterion for rejecting the null hypothesis* 5. Compute the test statistic* 6. Make a decision about the null hypothesis*

8 More on the Steps 1. Hypothesis: state both the null and alternative hypothesis. I like to denote the alternative hypothesis with a small a. 4. Criterion: Level of significance is based on the probability of making a Type I Error. The researcher sets this criterion

9 More on the Steps(2) 5. There are many test statistics that a researcher can use. The choice is based on the type of data you have, the hypothesis to be tested, the statistic of interest (mean, variances, correlations, proportions, etc), how the data were collected, assumptions about the population, and whether the population parameter is known.

10 More on the Steps(3) 5. continued: The basic formula for any test statistic is below. Test statistic = (statistic-parameter)/standard error of the statistic

11 Reject if... The test statistic falls in the specified region of the sampling distribution. Rejection of the null hypothesis leads one to believe that the alternative hypothesis is true; hence, the researcher INFERs that the scientific hypothesis is true.

12 Another View Remembering that basic formula: Test statistic = (statistic-parameter)/standard error of the statistic What is the magnitude of the difference between the observed statistic and the hypothesized parameter? If the difference is large, reject the null hypothesis (statistic falls in region of rejection) If the difference is small, do not reject (any difference is caused by random sampling fluctuations.