3.If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis.4.Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based onprobability laws; therefore, we can talk only in terms of non-absolute certainties.9.2 Outcomes and the Type I and Type II ErrorsIn every hypothesis test, the outcomes are dependent on a correct interpretation of the data. Incorrect calculations ormisunderstood summary statistics can yield errors that affect the results. AType Ierror occurs when a true null hypothesisis rejected. AType II erroroccurs when a false null hypothesis is not rejected.The probabilities of these errors are denoted by the Greek lettersαandβ, for a Type I and a Type II error respectively. Thepower of the test, 1 –β, quantifies the likelihood that a test will yield the correct result of a true alternative hypothesis beingaccepted. A high power is desirable.9.3 Distribution Needed for Hypothesis TestingIn order for a hypothesis test’s results to be generalized to a population, certain requirements must be satisfied.When testing for a single population mean:1.A Student'st-test should be used if the data come from a simple, random sample and the population is approximatelynormally distributed, or the sample size is large, with an unknown standard deviation.2.The normal test will work if the data come from a simple, random sample and the population is approximatelynormally distributed, or the sample size is large.When testing a single population proportion use a normal test for a single population proportion if the data comes from asimple, random sample, fill the requirements for a binomial distribution, and the mean number of success and the meannumber of failures satisfy the conditions:np> 5 andnq>nwherenis the sample size,pis the probability of a success, andqis the probability of a failure.9.4 Full Hypothesis Test ExamplesThehypothesis testitself has an established process. This can be summarized as follows:1.DetermineH0andHa. Remember, they are contradictory.2.Determine the random variable.3.Determine the distribution for the test.4.Draw a graph, calculate the test statistic, and if you choose then, use the test statistic to calculate thep-value. (Az-score and at-score are examples of test statistics.)5.Compare the calculated test statistic with the Z critical value determined by the level of confidence required by thetest and make a decision (cannot rejectH0or cannot acceptH0). Alternatively compare the preconceivedαwith thep-value, make a decision (cannot rejectH0or cannot acceptH0), and write a clear conclusion using English sentences.9.5 Rare Events, the Sample, Decision and ConclusionChapter 9 | Hypothesis Testing with One Sample383