(Round all intermediate calculations to at least 4 decimal places.) An entrepreneur owns some land that he wishes to develop. He identifies two development options: build condominiums or build apartment buildings. Accordingly, he reviews public records and derives the following summary measures concerning annual profitability based on a random sample of 34 for each such local business ventures. For the analysis, he uses a historical (population) standard deviation of $21,500 for condominiums and $19,500 for apartment buildings. (You may find it useful to reference the appropriate table: z table or t table) Sample 1 represents condominiums and Sample 2 represents apartment buildings. Condominiums Apartment Buildings x¯1x¯1 = $248,300 x¯2x¯2 = $235,300 n1 = 34 n2 = 34 a. Set up the hypotheses to test whether the mean profitability differs between condominiums and apartment buildings. multiple choice 1 H0: μ1 − μ2 = 0; HA: μ1 − μ2 ≠ 0 H0: μ1 − μ2 ≥ 0; HA: μ1 − μ2 < 0 H0: μ1 − μ2 ≤ 0; HA: μ1 − μ2 > 0 b. Calculate the value of the test statistic. (Round your answer to 2 decimal places.) c. Find the p-value. multiple choice 2 p-value < 0.01 p-value 0.10 0.05 p-value < 0.10 0.025 p-value < 0.05 0.01 p-value < 0.025 d-1. At the 10% significance level, what is the conclusion to the test?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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(Round all intermediate calculations to at least 4 decimal places.)

An entrepreneur owns some land that he wishes to develop. He identifies two development options: build condominiums or build apartment buildings. Accordingly, he reviews public records and derives the following summary measures concerning annual profitability based on a random sample of 34 for each such local business ventures. For the analysis, he uses a historical (population) standard deviation of $21,500 for condominiums and $19,500 for apartment buildings. (You may find it useful to reference the appropriate table: z table or t table)

Sample 1 represents condominiums and Sample 2 represents apartment buildings.

Condominiums	Apartment Buildings
x¯1x¯1 = $248,300	x¯2x¯2 = $235,300
n₁ = 34	n₂ = 34

a. Set up the hypotheses to test whether the mean profitability differs between condominiums and apartment buildings.

multiple choice 1

H₀: μ₁ − μ₂ = 0; H_A: μ₁ − μ₂ ≠ 0
H₀: μ₁ − μ₂ ≥ 0; H_A: μ₁ − μ₂ < 0
H₀: μ₁ − μ₂ ≤ 0; H_A: μ₁ − μ₂ > 0

b. Calculate the value of the test statistic. (Round your answer to 2 decimal places.)

c. Find the p-value.

multiple choice 2

p-value < 0.01
p-value

0.10
0.05

p-value < 0.10
0.025

p-value < 0.05
0.01

p-value < 0.025

d-1. At the 10% significance level, what is the conclusion to the test?

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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