Type I and Type II Errors

Question 165569 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)

Roman wants to testH0: p = 0.5Ha: p > 0.5where p = the true proportion of all babies who are longer than 20 inches, using the α = 0.01 significance level. What conclusion should Roman draw?

Answer

Because the P-value of 0.047 > α = 0.01, he should fail to reject H0. There is not convincing evidence that the true proportion of all babies who are over 20 inches is greater than 0.5.

Because the P-value of 0.047 > α = 0.01, he should reject H0. There is convincing evidence that the true proportion of all babies who are over 20 inches is greater than 0.5.

Because the P-value of 0.047 > α = 0.01, he should reject Ha. There is convincing evidence that the true proportion of all babies who are over 20 inches is greater than 0.5.

Because the P-value of 0.047 > α = 0.01, he should fail to reject Ha. There is not convincing evidence that the true proportion of all babies who are over 20 inches is greater than 0.5.

Explanation

Compare the P-value, 0.047, with the significance level, α = 0.01. Since 0.047 is greater than 0.01, the result is not statistically significant, so Roman should fail to reject H₀. There is not convincing evidence that the true proportion of all babies longer than 20 inches is greater than 0.5; this is choice A.

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