Answered: Question 14: Big houses: The U.S.…

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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Question 14: Big houses: The U.S. Census Bureau reported that the mean area of U.S. homes built in 2018 was 2559 square feet. Assume that a simple random sample of 22 homes built in 2020 had a mean area of 2654 square feet, with a standard deviation of 184 square feet. Assume the population of areas is normally distributed. Can you conclude that the mean area of homes built in 2020 is greater than that of homes built in 2018 ? Use the a=0.01 level of significance.

Part 1: (a) Find the P -value. Use the TI-84 calculator and round your answer to at least four decimal places.

The P-value is (BLANK)

Part 2: (b) What is the decision?

A. Reject H0

B. Do Not Reject H0

Part 3: (c) Interpret the result.

We ▼(Choose one) enough evidence at the 0.01 level of significance to conclude that the mean area of homes built in 2020▼(Choose one) that of homes built in 2018.

Answer Choice:

Have
Do Not Have

Answer Choice:

Is greater than
Is not equal to

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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