In a poll, the proportion of yes responses is tested whether it equals 0.50. Which test would you use?

In a poll, the proportion of yes responses is tested whether it equals 0.50. Which test would you use?

• A. One-Proportion Z-Test
• B. Two-Proportion Z-Test
• C. One-Sample T-Test
• D. Chi-Square Goodness-of-Fit Test

Answer: (A)

You’re evaluating whether a single population proportion matches a specific value, here 0.50. When you want to test a single proportion against a fixed value, the appropriate method is a one-proportion z-test, as long as the sample is large enough for the normal approximation. You compare the observed p-hat to the hypothesized p0 = 0.50 by standardizing the difference: z = (p-hat − 0.50) / sqrt[0.50(1−0.50)/n]. If the z statistic is far from zero, you have evidence that the true proportion differs from 0.50. This approach relies on random sampling and a sufficiently large n so that np0 and n(1−p0) are not too small; otherwise an exact binomial test would be more appropriate. The other options don’t fit as directly. A two-proportion z-test is for comparing proportions from two independent samples, not testing a single proportion against a fixed value. A one-sample t-test is used for a mean of a continuous variable, not a proportion. A chi-square goodness-of-fit test can assess whether observed category counts fit a specified distribution across several categories, which is broader than testing a single proportion against 0.50; the standard choice for this specific question is the one-proportion z-test.

You’re evaluating whether a single population proportion matches a specific value, here 0.50. When you want to test a single proportion against a fixed value, the appropriate method is a one-proportion z-test, as long as the sample is large enough for the normal approximation. You compare the observed p-hat to the hypothesized p0 = 0.50 by standardizing the difference: z = (p-hat − 0.50) / sqrt[0.50(1−0.50)/n]. If the z statistic is far from zero, you have evidence that the true proportion differs from 0.50. This approach relies on random sampling and a sufficiently large n so that np0 and n(1−p0) are not too small; otherwise an exact binomial test would be more appropriate.

The other options don’t fit as directly. A two-proportion z-test is for comparing proportions from two independent samples, not testing a single proportion against a fixed value. A one-sample t-test is used for a mean of a continuous variable, not a proportion. A chi-square goodness-of-fit test can assess whether observed category counts fit a specified distribution across several categories, which is broader than testing a single proportion against 0.50; the standard choice for this specific question is the one-proportion z-test.