Section 7.4 Hypothesis Testing for Proportions Larson/Farber 4th ed.

Section 7.4 Objectives Use the z-test to test a population proportion p Larson/Farber 4th ed.

z-Test for a Population Proportion A statistical test for a population proportion. Can be used when a binomial distribution is given such that np  5 and nq  5. The test statistic is the sample proportion. The standardized test statistic is z. Larson/Farber 4th ed.

Using a z-Test for a Proportion p 1.State the claim mathematically and verbally. Identify the null and alternative hypotheses. 2.Specify the level of significance. 3.Sketch the sampling distribution. 4.Determine any critical value(s). State H 0 and H a. Identify . Use Table 5 in Appendix B. Verify that np ≥ 5 and nq ≥ 5 Larson/Farber 4th ed. In WordsIn Symbols

Using a z-Test for a Proportion p 5.Determine any rejection region(s). 6.Find the standardized test statistic. 7.Make a decision to reject or fail to reject the null hypothesis. 8.Interpret the decision in the context of the original claim. If z is in the rejection region, reject H 0. Otherwise, fail to reject H 0. Larson/Farber 4th ed. In WordsIn Symbols

Example: Hypothesis Test for Proportions A research center estimates that no more than 40% of US adults eat breakfast every day. IN a random sample of 250 US adults, 41.6% say they eat breakfast every day. At α = 0.01, is there enough evidence to reject the researcher’s claim? Solution: Verify that np ≥ 5 and nq ≥ 5. p = 0.40 and q = 0.60 np = 250(0.40) = 100 and nq = 250(0.60) = 150 Larson/Farber 4th ed.

Solution: Hypothesis Test for Proportions H 0 : H a :  = Rejection Region: p ≤ 0.40 (claim) p > Decision: At the 1% level of significance, there is insufficient evidence to reject the researcher’s claim that no more than 40% of US adults eat breakfast every day. Test Statistic Fail to reject H 0 Larson/Farber 4th ed. z

Example: Hypothesis Test for Proportions 7.4, #12 - An environmentalist clams that more than 60% of british consumers are concerned about the use of genetic modification in food production and want to avoid genetically modified foods. You want to test this claim. You find that a random sample of 100 consumers, 65% say they are concerned about the use of genetically modified foods. At   ’  Solution: Verify that np ≥ 5 and nq ≥ 5. np = 100(0.60) = 60 and nq = 100 (0.40) = 40 Larson/Farber 4th ed.

Solution: Hypothesis Test for Proportions H 0 : H a :  = Rejection Region: p ≤ 0.60 p > Decision: At the 10% level of significance, there is not enough evidence to support the environmentalist’s claim. Test Statistic 1.02 z Fail to Reject H 0 Larson/Farber 4th ed.

Section 7.4 Summary Used the z-test to test a population proportion p HW: EO Larson/Farber 4th ed.

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