Unit 8 Section 8-1 & 8-2

8-2: Steps in Hypothesis Testing- Traditional Method  Hypothesis Testing – a decision making process for evaluating a claim about a population.  Hypotheses concerning parameters (such as mean or proportions) can be investigated.  Means : z-test or the t-test  Variance/Standard Deviation : chi-square test  Three methods used to test hypotheses:  Traditional Method  P-Value Method  Confidence Interval Method

 Statistical Hypothesis – conjecture about a population parameter.  May or may not be true. There are two types of statistical hypotheses:  Null Hypothesis – a statistical hypothesis that states there is no difference between a parameter and a specific value, or that there is no difference between two parameters.  Notation: H 0  Alternative Hypothesis – a statistical hypothesis that states the existence of a difference between a parameter and a specific value, or states that there is a difference between two parameters.  Notation: H 1 Section 8-2

 The critical or rejection region is the range of values of the test value that indicates that there is a significant difference and that the null hypothesis should be rejected.  The noncritical or nonrejection region is the range of values of the test value that indicates that the difference was probably due to chance and that the null hypothesis should not be rejected. Section 8-2

 One-tailed test – indicates that the null hypothesis should be rejected when the test value is in the critical region on one side of the mean.  A one-tailed test is either right-tailed or left- tailed, depending on the direction of the inequality of the alternative hypothesis.  Two-tailed test – the null hypothesis should be rejected when the test value is in either of the two critical regions. Section 8-2

Stating the Null and Alternative Hypothesis  Situation A.  Situation B.  Situation C. Section 8-2

Hypothesis Testing: Common Phrases Section 8-2 >< Is greater than Is above Is higher than Is longer than Is bigger than Is increased Is less than Is below Is lower than Is shorter than Is smaller than Is decreased or reduced from ≥≤ Is greater than or equal to Is at least Is not less than Is less than or equal to Is at most Is not more than =≠ Is equal to Is exactly the same as Has not changed from Is the same as Is not equal to Is different from Has changed from Is not the same as

After the hypothesis is stated, a researcher will then…  Select the correct statistical test  Choose an appropriate level of significance  Formulate a plan for conducting the study Section 8-2

 Statistical Test – uses the data obtained from a sample to make a decision about whether the null hypothesis should be rejected.  Test value – the numerical value obtained from a statistical test. Section 8-2

 Using a statistical test regarding mean as an example…we begin by comparing the data obtained from the sample with the data from the population.  We would then decide to either reject or not reject the null hypothesis (based on the value obtained from the statistical test).  If there is a significant difference, the null hypothesis is rejected. If there is not a significant difference, the null hypothesis is not rejected. Section 8-2

 There are four possible outcomes when determining to reject/not reject the null hypothesis: Section 8-2

 Two of the outcomes result in a correct decision, while two outcomes result in errors.  Type I Error – occurs if one rejects the null hypothesis when it is true.  Type II Error - occurs if one does not reject the null hypothesis when it is false. Section 8-2

 Example 2: In a jury trial, the defendant is either innocent or guilty. He or she will be either convicted or acquitted. Determine the null and alternative hypothesis. Complete the diagram below based on the information from the example.

 Level of Significance – the maximum probability of committing Type I Error.  The probability is symbolized as α  Note: the probability of committing Type II Error is symbolized by β. This cannot easily be computed.  Critical Value – separates the critical region from the noncritical region.  The symbol for critical value is C.V. Section 8-2

Homework:  Pg 404 : #’s Section 8-2