• Step five: make a decision. Only one of two decisions is possible in hypothesis testing —either accept or reject the null hypothesis. SUMMARY OF THE STEPS IN HYPOTHESIS TESTING: 1. Establish the null hypothesis and the alternate hypothesis 2. Select the level of significance/level of risk 3. Select an appropriate test statistic 4. Formulate a decision rule based on steps 1, 2, and 3 above. 5. Make a decision regarding the null hypothesis based on the sample information, interpret the results of the test. 10.5—ONE TAILED AND TWO TAILED TESTS OF SIGNIFICANCE A two-tailed test of significance is when the alternate hypothesis could either be greater than, or less than the null hypothesis. So there are two levels of risk/significance: one positive and one negative.
10.7—p-Value in Hypothesis Testing How confident are we in rejecting the null hypothesis? p-Value: the probability of observing a sample value as extreme as, or more extreme than, the value observed, given that the null hypothesis is true. If the p-value is smaller than the significance level, null hypothesis is rejected. If p-value is larger than the significance level, null hypothesis is not rejected. A very small p-value, such as .0001, indicates that there is little likelihood that H is true. On the other hand a p value of .2033 means that H is not rejected, and there is little likelihood that it is false. How do we compute the p-value? A p-value is a way to express the likelihood that the null hypothesis is false. 10.9—TESTS CONCERNING PROPORTIONS 10.10 TYPE II ERROR In a hypothesis testing situation there is the possibility that a null hypothesis is not rejected when it is actually false. Accepting a false null hypothesis is called a Type II Error. Type II Error is identified by the Greek letter Beta. CHAPTER 10—Summary of the Summary • A confidence interval is a range of values within which we expect the population parameter to occur. • A hypothesis is a statement about a population. Data are then used to check the reasonableness of the statement. • Hypothesis: a statement about a population parameter subject to verification. • In most cases, the population is so large that it is not feasible to study all the items, objects, or persons in the population. An alternative to measuring or interview the entire population is to take a sample from the population.
• Hypothesis testing starts with a statement or assumption about a population parameter—such as the population mean. This statement is referred to as a hypothesis. Based on certain decision rules, we accept or reject the hypothesis. • Hypothesis Testing: a procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement. • There is usually a “not” or a “no” term in the null hypothsis. • The null hypothesis is a statement that is not rejected unless our sample data provide convincing evidence that it is false. However, if the null hypothesis is not rejected on the basis of the sample data, we cannot say that the null hypothesis is true.
You've reached the end of your free preview.
Want to read all 12 pages?