7.4 Hypothesis Testing for Proportions

1. 7.4 Hypothesis Testing for Proportions Use a z-test to test a population proportion p

2. The z-test for a proportion is a statistical test for a population proportion p. The z-test can be used when a binomial distribution is given such that np ≥ 5 and nq≥ 5. The test statistic is the sample proportion and the standardized test statistic is z-Test for a Proportion p

3. A research center claims that more than 25% of U.S. adults have used a cellular phone to access the Internet. In a random sample of 125 adults, 32% say they have used a cellular phone to access the Internet. At α = 0.05, is there enough evidence to support the researcher’s claim? np = 31.25 > 5 and nq = 93.75 > 5 Critical value: 1.645; Rejection region: z > 1.645 z = 1.81 Reject the null hypothesis There is enough evidence at the 5% level of significance to support the claim that more than 25% of U.S. adults have used a cellular phone to access the internet. Try it yourself 1 Hypothesis Test for a Proportion

4. A research center claims that 30% of U.S. adults have not purchased a certain brand because they found the advertisements distasteful. You decide to test this claim and ask a random sample of 250 U.S. adults whether they have not purchased a certain brand because they found the advertisements distasteful. Of those surveyed, 36% reply yes. At α = 0.10, is there enough evidence to reject the claim? np = 75 > 5 and nq = 175 > 5 Critical values: ±1.645; Rejection regions: z < -1.645, z > 1.645 z = 2.07 Reject the null hypothesis There is enough evidence at the 10% level of significance to reject the claim that 30% of U.S. adults have not purchased a certain brand because they found the advertisements distasteful. Try it yourself 2 Hypothesis Test for a Proportion