At a roadblock, tickets were issued for expired inspection stickers to 22 of 628 cars stopped. Based on this sample, estimate the proportion of autos in the region with expired inspections.

At a roadblock, tickets were issued for expired inspection stickers to 22 of 628 cars stopped. Based on this sample, estimate the proportion of autos in the region with expired inspections.

• A. 1-Proportion Z-Interval
• B. 2-Proportion Z-Interval
• C. Paired T-Test
• D. Chi-Square Test

Answer: (A)

The main idea is estimating a population proportion with a confidence interval. From the sample, the proportion with expired inspections is p-hat = 22/628 ≈ 0.035 (3.5%). To form a one-proportion z-interval, use the standard error sqrt(p-hat(1−p-hat)/n). This is about sqrt(0.0350 × 0.9650 / 628) ≈ 0.00734. For a typical 95% confidence level, the margin of error is z* × SE ≈ 1.96 × 0.00734 ≈ 0.0144. So the interval is 0.035 ± 0.0144, i.e., roughly (0.021, 0.049), about 2.1% to 4.9%. This approach is the best choice because it’s specifically designed to estimate a single population proportion from a single sample. The other options are used for different problems: a two-proportion interval compares proportions from two groups; a paired t-test compares means of paired data; and a chi-square test assesses relationships or goodness-of-fit, not a single-proportion estimate with a confidence interval.

The main idea is estimating a population proportion with a confidence interval. From the sample, the proportion with expired inspections is p-hat = 22/628 ≈ 0.035 (3.5%). To form a one-proportion z-interval, use the standard error sqrt(p-hat(1−p-hat)/n). This is about sqrt(0.0350 × 0.9650 / 628) ≈ 0.00734. For a typical 95% confidence level, the margin of error is z* × SE ≈ 1.96 × 0.00734 ≈ 0.0144. So the interval is 0.035 ± 0.0144, i.e., roughly (0.021, 0.049), about 2.1% to 4.9%.

This approach is the best choice because it’s specifically designed to estimate a single population proportion from a single sample. The other options are used for different problems: a two-proportion interval compares proportions from two groups; a paired t-test compares means of paired data; and a chi-square test assesses relationships or goodness-of-fit, not a single-proportion estimate with a confidence interval.