![]() ![]() Where is the sample proportion, is the upper z‐value corresponding to half of the desired alpha level, and n is the sample size.Ī sample of 100 voters selected at random in a congressional district prefer Candidate Smith to Candidate Jones by a ratio of 3 to 2. The z‐value may now be calculated:įrom the z‐table, you find that the probability of a z‐value less than 0.97 is 0.834, so we do not reject the null hypothesis, so it cannot be concluded at that level of significance that the population of runners is at least 40 percent women. The proportion of women runners in the sample is 32 out of 70, or 45.7 percent. Were their recruitment efforts successful? The sponsors would like to be 90 percent certain that at least 40 percent of the participants are women. A sample of 70 runners is taken, of which 32 are women. ![]() The sponsors of a city marathon have been trying to encourage more women to participate in the event. The test is most accurate when π (the population proportion) is close to 0.5 and least accurate when π is close to 0 or 1. Because the distribution of sample proportions is approximately normal for large samples, the z statistic is used. Where is the sample proportion, π 0is the hypothesized proportion, and n is the sample size. Online Quizzes for CliffsNotes Statistics QuickReview, 2nd Edition.Quiz: Test for Comparing Two Proportions.Quiz: Test for a Single Population Proportion.Test for a Single Population Proportion.Quiz: Two-Sample t-test for Comparing Two Means.Two Sample t test for Comparing Two Means.Quiz: Two-Sample z-test for Comparing Two Means.Quiz: Introduction to Univariate Inferential Tests.Two-Sample z-test for Comparing Two Means. ![]() Quiz: Point Estimates and Confidence Intervals.Point Estimates and Confidence Intervals.Quiz: Normal Approximation to the Binomial.Quiz: Populations, Samples, Parameters, and Statistics.Populations, Samples, Parameters, and Statistics.Quiz: Introduction to Numerical Measures. ![]()
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