The average teaching salary in Georgia is $48,553 per year. The school districts in the metro Atlanta area boast that they pay more. A company that is running a career fair decides to take a random sample of 228 teachers from the metro Atlanta area and record their salaries. The sample mean is $49,021, with a standard deviation of $3,127. Do the data provide statistically significant evidence at the α = 0.05 level that the average teaching salary in the metro Atlanta area is greater than the state average?The P-value of this test is 0.0124.What is the correct interpretation of the P-value?There is a 1.24% chance that the mean teaching salary in metro Atlanta is greater than $48,553.Assuming that the mean teaching salary is $48,553, there is a 1.24% chance that the null hypothesis is true.Assuming that the mean teaching salary is greater than $48,553, there is a 1.24% probability of getting a sample mean salary of $49,021 or more by chance alone.Assuming that the mean teaching salary is $48,553, there is a 1.24% probability of getting a sample mean salary of $49,021 or more by chance alone.

Given : The P-value of this test is 0.0124.

Answered: The average teaching salary in Georgia…

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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The average teaching salary in Georgia is $48,553 per year. The school districts in the metro Atlanta area boast that they pay more. A company that is running a career fair decides to take a random sample of 228 teachers from the metro Atlanta area and record their salaries. The sample mean is $49,021, with a standard deviation of $3,127. Do the data provide statistically significant evidence at the α = 0.05 level that the average teaching salary in the metro Atlanta area is greater than the state average?

The P-value of this test is 0.0124.

What is the correct interpretation of the P-value?

There is a 1.24% chance that the mean teaching salary in metro Atlanta is greater than $48,553.

Assuming that the mean teaching salary is $48,553, there is a 1.24% chance that the null hypothesis is true.

Assuming that the mean teaching salary is greater than $48,553, there is a 1.24% probability of getting a sample mean salary of $49,021 or more by chance alone.

Assuming that the mean teaching salary is $48,553, there is a 1.24% probability of getting a sample mean salary of $49,021 or more by chance alone.

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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