Type I error: Reject a true null hypothesisType II error: Do not reject a false null hypothesis.P(Type I error) = αP(Type II error) = β11.49

Inferential Statistics •Used to make inferences about a population from a sample of that population.•Drawing conclusions and/or making decisions concerning a population based only on sample data.

Hypothesis Testing •A statistical hypothesis is an assumption about a population parameter. This assumption may or may not be true.•Hypothesis testing refers to the formal procedures used by statisticians to accept or reject statistical hypotheses.–The best way to determine whether a statistical hypothesis is true would be to examine the entire population. Since that is often impractical, researchers typically examine a random sample from the population.–E.g., policy making, new drug development, opinion survey…–Big data may make a difference…–If sample data are not consistent with the statistical hypothesis, the hypothesis is rejected.

Concepts of Hypothesis Testing (1) There are twohypotheses. One is called the null hypothesisand the other the alternativeor research hypothesis. The usual notation is:H0: — the ‘null’ hypothesisH1: — the ‘alternative’ or ‘research’ hypothesisThe null hypothesis (H0) will always state that the parameter equalsthe valuespecified in the alternative hypothesis (H1)pronounced H “nought” 11.52

Concepts of Hypothesis Testing Consider Example 10.1 (mean demand for computers during assembly lead time) again. Rather than estimate the mean demand, our operations manager wants to know whether the mean is different from 350 units. We can rephrase this request into a test of the hypothesis:H0:μ = 350Thus, our research hypothesis becomes:H1:μ ≠350This is what we are interested in determining… 11.53

Concepts of Hypothesis Testing (2) The testing procedure begins with the assumption that the null hypothesis is true.Thus, until we have further statistical evidence, we will assume:H0: = 350 (assumed to be TRUE)11.54

Concepts of Hypothesis Testing (3) The goalof the process is to determine whether there is enough evidenceto infer that the alternative hypothesis is true.That is, is there sufficient statistical information to determine if this statement is true?H1:μ ≠350 This is what we are interested in determining… 11.55

Concepts of Hypothesis Testing (4) There are twopossible decisions that can be made:Conclude that there is enough evidenceto support the alternative hypothesis(also stated as: rejecting the null hypothesis in favor of the alternative)Conclude that there is not enough evidenceto support the alternative hypothesis(also stated as: notrejecting the null hypothesis in favor of the alternative)NOTE: we do notsay that we acceptthe null hypothesis…11.56

Concepts of Hypothesis Testing Once the null and alternative hypotheses are stated, the next step is to randomly sample the population and calculate a test statistic(in this example, the sample mean).