Compute Probabilities of a Sample Proportion
-The National Association of Realtors estimates that 23% of all homes purchased in 2004 were considered investment properties. If a sample of 800 homes sold in 2004 is obtained and it was noted that 248 homes were to be used as investment property, would this be unusual Answer Yes or No.
A) Yes
B) No

Question

Quizplus · Accepted Answer

The sample proportion is 248/800 = 0.31. The expected proportion is 0.23. The standard deviation of the sample proportion is sqrt[(0.23)(0.77)/800] ≈ 0.015. The z-score is (0.31 - 0.23) / 0.015 ≈ 5.33, which is significantly higher than typical z-scores for usual events (usually within ±2). Hence, it is unusual.