The Western blot assay is a blood test for the presence of HIV. It has been found that this test sometimes gives false positive results for HIV. A medical researcher claims that the rate of false positives is 2%. A recent study of 300 randomly selected U.S. blood donors who do not have HIV found that 3 received a false positive test result. At ? = 0.05, is there enough evidence to reject the researcher's claim? (Show complete work for all the guidelines shown on page 388 of the class textbook).

in 22WNCMP MAT-200-20103: Wee X in 22WNCMP MAT-200-20103: MyL X e Text P 7.4 Hypothesis Testing for Propor + X C plus.pearson.com/courses/seitz77133/products/128233/pages/418?locale=&platformld=1030&iesCode=ECP6v88ouY Update Apps NO LAR Z Sy CT WSJ - W W = Reading list 7 Hypothesis Testing with One Sample AC n 7.4 Hypothesis Testing for Proportions (o> What You Should Learn Hypothesis Test for Proportions Q How to use the z-test to test a population proportion p Hypothesis Test for Proportions In Sections 7.2 and 7.3, you learned how to perform a hypothesis test for a population mean u. In this section, you will learn how to test a population proportion p. Hypothesis tests for proportions can be used when politicians want to know the proportion of their constituents who favor a certain bill or when quality assurance engineers test the proportion of parts that are defective. AA If np 2 5 and nq 2 5 for a binomial distribution, then the sampling distribution for p is approximately normal with a mean of up = p and a standard error of Up = Vpq. z-Test for a Proportion p The z-test for a proportion p is a statistical test for a population proportion. The z-test can be used when a binomial distribution is given such that np 2 5 and nq 2 5. The test statistic is the sample proportion p and the standardized test statistic is P - up _ P - P Z = Standardized test statistic for p X op Vpq22WNCM P M AT-ZUU-Z X EZWNCMF' Mi": - x 'P 7.4 Hypothe SIS Testing for Prop C plus. pear'soncom @L H: . .; "69 '-".-l 7 Hypothesis Testing with One Sample I] Ac E) test statistic is - - V ' Slanda rdized tesl statistic for p (0) GUIDELINES Using I z-Test for 3 Proportion p In Words In Symbols L Verify that the sampling distribution np 2 5, nq 2 5 of F5 can be approximated by a normal distribution. 2. State the claim mathematically State H0 and HR. and verbally. Identify the null and alternative hypotheses. PQEO l Ti 5 "dv P 3. Specify the level of signicance. Identify a. A hypotheSIs test for a . A . . . proportion p can also be 4. Determine the critical value(s). Use Table 4 1n Appendix B. performed using Pvalues 5. Determine the rejection region(s). Use the guidelines on . . . P P . 6. Flnd the standardized test statistic z = l foes: ifessgrzjgezfiws and sketch the sampling distribution. V P4 /" but in Step 4 find the standardized. 7. Make a decision to reject or fail to If 2 is in the rejection region, test statistic by using the formula reject the null hypothesis. then reject Hg. Otherwise, A _ fail to reject H\". z = p p . 8. Interpret the decision in the context V m/ n of the original claim. The other steps in the test are the also test a claim using Pvalues, as shown in the Study Tip at the left