A national marketing campaign increases name-brand recognition. After campaign, 135 of 500 recognize the brand; baseline recognition is 0.23. Which test is appropriate to determine whether recognition increased?

A national marketing campaign increases name-brand recognition. After campaign, 135 of 500 recognize the brand; baseline recognition is 0.23. Which test is appropriate to determine whether recognition increased?

• A. 2-proportion z-test
• B. 1-proportion z-test
• C. Chi-square test of independence
• D. Paired t-test

Answer: (B)

This question tests whether a sample proportion after the campaign differs from a known baseline proportion. The baseline recognition is 0.23, and after the campaign, 135 of 500 people recognize the brand, giving a sample proportion of 0.27. To determine if this observed post-campaign proportion is significantly larger than the baseline, use a one-proportion z-test that compares the observed proportion to a fixed hypothesized value. Compute the standard error under the null: SE = sqrt(p0(1-p0)/n) = sqrt(0.23 × 0.77 / 500) ≈ 0.0188. The test statistic is z = (phat − p0) / SE = (0.27 − 0.23) / 0.0188 ≈ 2.13. This yields a one-sided p-value around 0.02, indicating a statistically significant increase at common alpha levels like 0.05. The other tests aren’t appropriate here. A two-proportion z-test would compare two separate sample proportions, not a sample proportion against a known baseline. A chi-square test of independence looks at relationships between two categorical variables in a contingency table, not testing a single proportion against a fixed value. A paired t-test is for comparing means of paired continuous data, not proportions.

This question tests whether a sample proportion after the campaign differs from a known baseline proportion. The baseline recognition is 0.23, and after the campaign, 135 of 500 people recognize the brand, giving a sample proportion of 0.27. To determine if this observed post-campaign proportion is significantly larger than the baseline, use a one-proportion z-test that compares the observed proportion to a fixed hypothesized value.

Compute the standard error under the null: SE = sqrt(p0(1-p0)/n) = sqrt(0.23 × 0.77 / 500) ≈ 0.0188. The test statistic is z = (phat − p0) / SE = (0.27 − 0.23) / 0.0188 ≈ 2.13. This yields a one-sided p-value around 0.02, indicating a statistically significant increase at common alpha levels like 0.05.

The other tests aren’t appropriate here. A two-proportion z-test would compare two separate sample proportions, not a sample proportion against a known baseline. A chi-square test of independence looks at relationships between two categorical variables in a contingency table, not testing a single proportion against a fixed value. A paired t-test is for comparing means of paired continuous data, not proportions.