Question 17 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
A real-estate agent conducted an experiment to test the effect of selling a staged home vs. selling an empty home. To do so, the agent obtained a list of 10 comparable homes just listed for sale that were currently empty. He randomly assigned 5 of the homes to be "staged,” meaning they were filled with nice furniture and decorated. The owners of the 5 homes all agreed to have their homes staged by professional decorators. The other 5 homes remained empty. The hypothesis is that empty homes are not as appealing to buyers as staged homes and, therefore, sell for lower prices than staged homes. The mean selling price of the 5 empty homes was $150,000 with a standard deviation of $22,000. The mean selling price of the 5 staged homes was $175,000 with a standard deviation of 35,000. A dotplot of each sample shows no strong skewness and no outliers.
Answer
A
H0: μ1 – μ2 = 0, Ha: μ1 – μ2 < 0
B
H0: μ1 – μ2 = 0, Ha: μ1 – μ2 > 0
C
H0: x̄1 – x̄2 = 0, Ha: x̄1 – x̄2 < 0
D
H0: x̄1 – x̄2 = 0, Ha: x̄1 – x̄2 > 0
Explanation
Let μ1 be the mean selling price for comparable empty homes and μ2 the mean selling price for comparable staged homes. The hypothesis says empty homes sell for less, so the alternative is μ1 − μ2 < 0. The null states there is no difference in the population mean prices, μ1 − μ2 = 0; choice A uses population means rather than the observed sample means.
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