A real-estate agent conducted an experiment to test the effect 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 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 dollars comma 000 with a standard deviation of 22 dollars comma 000 The mean selling price of the 5 staged homes was 175 dollars comma 000 with a standard deviation of 35 comma 000 A dotplot of each sample shows no strong skewness and no outliers. The agent tests ratio of cap h sub 0 to mu sub 1 minus mu sub 2 is equal to 0 , ratio of cap h sub A to mu sub 1 minus mu sub 2 is less than 0 , where mu sub 1 is equal to the true mean selling price of all comparable empty homes and mu sub 2 is equal to the true mean selling price of all comparable staged homes. The conditions for inference are met. The standardized test statistic is t is equal to negative 1 point 3 5 , and the cap p -value is between 0 point 1 0 and 0 point 1 5 What conclusion should be made using the significance level, alpha is equal to 0 point 1 0 ?
Answer
A
Fail to reject cap h sub 0 . There is not convincing evidence that the true mean selling price of all comparable empty homes is less than the true mean selling price of all comparable staged homes.
B
Fail to reject cap h sub 0 . There is convincing evidence that the true mean selling price of all comparable empty homes is less than the true mean selling price of all comparable staged homes.
C
Reject cap h sub 0 . There is not convincing evidence that the true mean selling price of all comparable empty homes is less than the true mean selling price of all comparable staged homes.
D
Reject cap h sub 0 . There is convincing evidence that the true mean selling price of all comparable empty homes is less than the true mean selling price of all comparable staged homes.
Explanation
The p-value is between 0.10 and 0.15, so it is greater than the significance level α = 0.10. Therefore, we fail to reject the null hypothesis. The results do not provide convincing evidence that the true mean selling price of comparable empty homes is less than that of comparable staged homes, which is choice A.
AI-written and checked against the verified answer.