You want to test if more than 20% of homes in a neighborhood have recently been sold through a short sale, at a foreclosure auction, or by the bank following an unsuccessful foreclosure auction. You take a sample of 60 homes from this neighborhood and find that 14 fit your criteria. The appropriate null and alternative hypotheses are ________. A) H₀: ≤ 0.23, H_A: 0.23 B) H₀: = 0.23, H_A: ≠ 0.23 C) H₀: p ≤ 0.20, H_A: p 0.20 D) H₀: p = 0.20, H_A: p ≠ 0.20

Question

You want to test if more than 20% of homes in a neighborhood have recently been sold through a short sale, at a foreclosure auction, or by the bank following an unsuccessful foreclosure auction. You take a sample of 60 homes from this neighborhood and find that 14 fit your criteria. The appropriate null and alternative hypotheses are ________. A) H₀: ≤ 0.23, H_A: > 0.23 B) H₀: = 0.23, H_A: ≠ 0.23 C) H₀: p ≤ 0.20, H_A: p > 0.20 D) H₀: p = 0.20, H_A: p ≠ 0.20

Quizplus · Accepted Answer

The null hypothesis should state that the proportion is less than or equal to 20%, so H₀: p ≤ 0.20 is appropriate. The alternative hypothesis should state that the proportion is greater than 20%, so H_A: p > 0.20 is also appropriate. Option A has a typo and does not specify the proportion correctly. Option B suggests that the null hypothesis is equal to 0.23, which is not correct. Option D has the same issue as option B, and also uses a point estimate instead of a range.

You Want to Test If More Than 20% of Homes