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 = 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 conclusion should be made?Use = 0.05.Because the P-value is = 0.05, we H0. We convincing evidence to conclude that the true mean teaching salary in the metro Atlanta area is the state average. ### Educational Website Content: Hypothesis Testing in Metro Atlanta Teaching Salaries**Introduction to the Scenario:**In Georgia, the average teaching salary is $48,553 per year. However, school districts in the metro Atlanta area claim that they pay more than this average. A company conducting a career fair collected a random sample of 228 teacher salaries from this region. The results showed a sample mean of $49,021 with a standard deviation of $3,127.**Statistical Question:**Do these 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?**Understanding the Hypothesis Test:****Given Data:**- **State Average Salary:** $48,553- **Sample Mean Salary:** $49,021- **Sample Standard Deviation:** $3,127- **Sample Size:** 228- **Significance Level (α):** 0.05**P-value and Conclusion:**- **P-value for the Test:** 0.0124**Decision Making:**To determine statistical significance, compare the P-value to the significance level:1. **Use α = 0.05.**2. Because the **P-value (0.0124)** is **less than** α = 0.05, we **reject** the null hypothesis (H₀).3. This result provides convincing evidence to conclude that the true mean teaching salary in the metro Atlanta area is **greater than** the state average.**Conclusion:**The analysis suggests that teachers in the metro Atlanta area earn more on average than the state-wide teaching salary of $48,553, providing validation to the claims made by the metro Atlanta school districts.

Answered: Image /qna-images/answer/8ff372ec-9300-4cc1-93cb-70a896f7ed35.jpgThe P-value of this test is 0.0124. The conclusion is, Because the P-value is 0.0124 is less than α=0.05, we reject H0. We provide statistically convincing evidence to conclude that the true mean teaching salary in the metro Atlanta area is greater than the state average.

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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Question

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 = 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 conclusion should be made?

Use = 0.05.
Because the P-value is = 0.05, we H₀. We convincing evidence to conclude that the true mean teaching salary in the metro Atlanta area is the state average.

### Educational Website Content: Hypothesis Testing in Metro Atlanta Teaching Salaries

**Introduction to the Scenario:**

In Georgia, the average teaching salary is $48,553 per year. However, school districts in the metro Atlanta area claim that they pay more than this average. A company conducting a career fair collected a random sample of 228 teacher salaries from this region. The results showed a sample mean of $49,021 with a standard deviation of $3,127.

**Statistical Question:**

Do these 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?

**Understanding the Hypothesis Test:**

**Given Data:**
- **State Average Salary:** $48,553
- **Sample Mean Salary:** $49,021
- **Sample Standard Deviation:** $3,127
- **Sample Size:** 228
- **Significance Level (α):** 0.05

**P-value and Conclusion:**

- **P-value for the Test:** 0.0124

**Decision Making:**

To determine statistical significance, compare the P-value to the significance level:

1. **Use α = 0.05.**
2. Because the **P-value (0.0124)** is **less than** α = 0.05, we **reject** the null hypothesis (H₀).
3. This result provides convincing evidence to conclude that the true mean teaching salary in the metro Atlanta area is **greater than** the state average.

**Conclusion:**

The analysis suggests that teachers in the metro Atlanta area earn more on average than the state-wide teaching salary of $48,553, providing validation to the claims made by the metro Atlanta school districts.

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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