A soccer player sets a goal to improve his kicking accuracy from 50%. After 12 kicks, he makes 10. Which test is appropriate to assess this proportion?

A soccer player sets a goal to improve his kicking accuracy from 50%. After 12 kicks, he makes 10. Which test is appropriate to assess this proportion?

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

Answer: (D)

Testing a single proportion against a hypothesized value is what this scenario calls for. You’re asking whether the player’s true kicking accuracy differs from the stated goal of 50%, based on one sample of 12 kicks. The appropriate method is the 1-proportion z-test. You compute phat as 10/12 ≈ 0.833, compare it to p0 = 0.50, and use the standard error sqrt[p0(1−p0)/n] = sqrt(0.25/12) ≈ 0.144. The z statistic is (phat − p0) / SE ≈ (0.833 − 0.50) / 0.144 ≈ 2.31. This gives a p-value around 0.02 for a two-sided test, suggesting the observed proportion is significantly different from 50% at conventional levels. The other options aren’t the right fit here: a two-proportion test compares two independent groups, a paired test is for matched data, and a chi-square test is typically used for independence/grequency fits at a broader level rather than testing a single hypothesized proportion.

Testing a single proportion against a hypothesized value is what this scenario calls for. You’re asking whether the player’s true kicking accuracy differs from the stated goal of 50%, based on one sample of 12 kicks. The appropriate method is the 1-proportion z-test. You compute phat as 10/12 ≈ 0.833, compare it to p0 = 0.50, and use the standard error sqrt[p0(1−p0)/n] = sqrt(0.25/12) ≈ 0.144. The z statistic is (phat − p0) / SE ≈ (0.833 − 0.50) / 0.144 ≈ 2.31. This gives a p-value around 0.02 for a two-sided test, suggesting the observed proportion is significantly different from 50% at conventional levels. The other options aren’t the right fit here: a two-proportion test compares two independent groups, a paired test is for matched data, and a chi-square test is typically used for independence/grequency fits at a broader level rather than testing a single hypothesized proportion.