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, = 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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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, H_a: 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, = 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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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