A random sample of 88 students found 14 who cheated; to test whether the true cheating rate is greater than 0.10, which statistical test should be used?

A random sample of 88 students found 14 who cheated; to test whether the true cheating rate is greater than 0.10, which statistical test should be used?

• A. 2-proportion z-test
• B. 1-proportion z-test
• C. Chi-square test of independence
• D. T-test for a single mean

Answer: (B)

This item tests whether a single population proportion exceeds a specified value using a one-proportion z-test. The observed proportion is 14/88 ≈ 0.159, and the null value is p0 = 0.10. Under the null, the standard error is sqrt(p0(1−p0)/n) = sqrt(0.1×0.9/88) ≈ 0.032. The z statistic is (0.159 − 0.10) / 0.032 ≈ 1.85. For a one-sided test, the p-value is about 0.03, which is below 0.05, so there is evidence that the true cheating rate is greater than 0.10. The test is appropriate here because we’re assessing a proportion from a single sample, and the sample size is large enough (np0 and n(1−p0) are both at least 5) for the normal approximation to be reasonable. The other tests don’t fit: a two-proportion z-test compares two proportions from two samples; a chi-square test of independence looks at relationships between two categorical variables; and a t-test for a single mean is used for a continuous outcome, not a proportion.

This item tests whether a single population proportion exceeds a specified value using a one-proportion z-test. The observed proportion is 14/88 ≈ 0.159, and the null value is p0 = 0.10. Under the null, the standard error is sqrt(p0(1−p0)/n) = sqrt(0.1×0.9/88) ≈ 0.032. The z statistic is (0.159 − 0.10) / 0.032 ≈ 1.85. For a one-sided test, the p-value is about 0.03, which is below 0.05, so there is evidence that the true cheating rate is greater than 0.10.

The test is appropriate here because we’re assessing a proportion from a single sample, and the sample size is large enough (np0 and n(1−p0) are both at least 5) for the normal approximation to be reasonable. The other tests don’t fit: a two-proportion z-test compares two proportions from two samples; a chi-square test of independence looks at relationships between two categorical variables; and a t-test for a single mean is used for a continuous outcome, not a proportion.