Respuesta :
By using the significance level, α = 0.10, the conclusion which should be made is that: D. Fail to reject H₀. 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.
What is a null hypothesis?
A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (Ha) and it asserts that two (2) possibilities are the same.
For an experiment to test the effect of selling a staged home versus selling an empty home, the appropriate null and alternative hypotheses would be given by:
- H₀: μ₁ - μ₂ = 0.
- Ha: μ₁ - μ₂ < 0.
where:
- μ₁ represents the true mean selling price of all comparable empty homes.
- μ₂ represents the true mean selling price of all comparable staged homes.
How to calculate value of the test statistic?
The test statistic can be calculated by using this formula:
[tex]t=\frac{x\;-\;u}{\frac{\sigma}{\sqrt{n} } }[/tex]
Where:
- x is the sample mean.
- u is the mean.
- is the standard deviation.
- n is the number of homes.
Based on the information provided, the standardized test statistic is equal to -1.35, and the P-value is between 0.10 and 0.15, we fail to reject null hypothesis (H₀).
Since the null hypothesis (H₀) is not rejected, we can reasonably infer and logically conclude that "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."
Read more on null hypothesis here: https://brainly.com/question/14913351
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Complete Question:
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 $150,000 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.
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. The conditions for inference are met. The standardized test statistic is t = –1.35, and the P-value is between 0.10 and 0.15. What conclusion should be made using the significance level, Alpha = 0.10?
A. Reject H0. 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.
B. Reject H0. 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.
C. Fail to reject H0. 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.
D. Fail to reject H0. 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.
