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Description: A sample of 510 homes for sale in ABC City showed a man asking price of $258,000, but the city claimed that the mean asking price for the population was $249,000. The population standard deviation of all homes for sale was $9000. Use the p-value appr

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 sample of 510 homes for sale in ABC City showed a man asking price of $258,000, but the city claimed that the mean asking price for the population was $249,000. The population standard deviation of all homes for sale was $9000. Use the p-value approach to conduct a full hypothesis test that can be used to determine whether the mean asking price is significantly greater than $249'ppp. Let a=.05

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 + ...

Expert Solution

Step 1

Given Information :

The provided sample mean is $\bar X = 249,000$ and the known population standard deviation is $σ = 9000$ , and the sample size is $n = 510$ .

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: Mean asking price is equal to $249,000 .

$i.e. μ = 258, 000$

Ha: Mean asking price is greater than $249'ppp

$i.e. μ < 258, 000$

This corresponds to a left-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

Step 2

Rejection Region

Based on the information provided, the significance level is $\alpha = 0.05$ , and the critical value for a left-tailed test is $z_c = -1.64$ .

The rejection region for this left-tailed test is $R = \{z: z < -1.64\}$

Test Statistics

The z-statistic is computed as follows:

Test Statistic = -0.023

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