A homeowners association wants to test if 75% of residents favor an amendment; sample 310 of 430 are in favor. Which test is used?

A homeowners association wants to test if 75% of residents favor an amendment; sample 310 of 430 are in favor. Which test is used?

• A. Two-Sample Z-Test
• B. Two-Proportion Z-Test
• C. Chi-Square Test
• D. One-Proportion Z-Test

Answer: (D)

This is a test of a single population proportion against a specified value. Here the goal is to determine whether the true proportion of residents who favor the amendment equals 75%. With one sample of 430 residents and 310 in favor, the observed proportion is about 0.721. Because you’re comparing one proportion to a known value (0.75) using a sizable sample, the standard approach is a one-proportion z-test. The test statistic is z = (p-hat − p0) / sqrt(p0(1 − p0)/n). The large-sample condition np0 and n(1 − p0) are satisfied, so the normal approximation is appropriate. The other options are for different scenarios: a two-sample z-test compares two proportions from two groups; a chi-square test is used for goodness-of-fit or independence with categorical data but is not the direct choice for testing a single proportion against a fixed value; a two-proportion z-test compares two independent proportions. Therefore, the one-proportion z-test is the correct method.

This is a test of a single population proportion against a specified value. Here the goal is to determine whether the true proportion of residents who favor the amendment equals 75%. With one sample of 430 residents and 310 in favor, the observed proportion is about 0.721. Because you’re comparing one proportion to a known value (0.75) using a sizable sample, the standard approach is a one-proportion z-test. The test statistic is z = (p-hat − p0) / sqrt(p0(1 − p0)/n). The large-sample condition np0 and n(1 − p0) are satisfied, so the normal approximation is appropriate. The other options are for different scenarios: a two-sample z-test compares two proportions from two groups; a chi-square test is used for goodness-of-fit or independence with categorical data but is not the direct choice for testing a single proportion against a fixed value; a two-proportion z-test compares two independent proportions. Therefore, the one-proportion z-test is the correct method.