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 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 five staged homes was $175,000 with a standard deviation of 35,000. A dotplot of each sample shows no strong skewness and no outliers. The agent tests H0: μ1 – μ2 = 0, Ha: μ1 – μ2 < 0, where μ1 = the true mean selling price of all comparable empty homes and μ2 = the true mean selling price of all comparable staged homes. Are the conditions for inference met for carrying out a t-test for a difference in means?

A t-test is a hypothesis-testing technique for analyzing the means of one or two populations. A t-test can be used to see if a single group differs from a known value, if two groups differ from each other (an independent two-sample t-test), or if paired measurements show a significant difference.

We have:

Null hypothesis:H0: μ1 – μ2 = 0,

Alternative hypothesis: Ha: μ1 – μ2 < 0

As it is mentioned that the samples are drawn randomly and mentioned that no skewness is observed, this Indicates that the distribution is approximately normal

The total number of readings = 10

Which is not more than 10% of the Population size.

Thus, the statement "Yes, all the conditions for Inference have been met" is correct.

Learn more about the t-test here:

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