### Hypothesis Tests for the Difference Between Two Population MeansA real estate agent believes that the mean home price in the northern part of a county is higher than the mean price in the southern part of the county and would like to test the claim. A simple random sample of housing prices is taken from each region. The results are shown below.#### Data Summary:| | Southern | Northern ||----------------------------|----------|----------|| **Mean** | 155.056 | 168.889 || **Variance** | 345.938 | 560.928 || **Observations** | 18 | 18 || **Pooled Variance** | 453.433 | || **Hypothesized Mean Difference** | 0 | || **Degrees of Freedom (df)** | 34 | || **t Stat** | 1.949 | || **P(T<=t) one-tail** | 0.030 | || **t Critical one-tail** | 2.441 | || **P(T<=t) two-tail** | 0.060 | || **t Critical two-tail** | 2.728 | || **Confidence Level** | 99% | |#### Graph ExplanationThe graph shown represents the distribution of the t-statistic. The t-statistic distribution is illustrated with a smooth curve, showcasing a peak at the mean of zero and two tails extending in the negative and positive directions.- The x-axis represents the t-values ranging from -3 to 3.- The y-axis represents the probability density.Key points marked on the graph:- The calculated t-value (t = 1.949) is shown towards the right side of the distribution.- The areas under the curve in the tails represent the p-values for the one-tail and two-tail tests.#### Additional Calculations:- **Sample Size (n)**: Ex = 9- **Degrees of Freedom (df)**: (Calculation needed)- **Point Estimate for the Southern Part of the County (\( \bar{x}_1 \))**: Ex = 1.234- **Point Estimate for the Northern Part of the County (\( \bar{x}_2 \))**: (Calculation needed)

Mean Variance Observations Pooled Variance Hypothesized Mean Difference df t Stat P[T<=t) one-tail t Critical one-tail P[T<=t) two-tail t Critical two-tail Confidence Level Southern Northern 155.056 168.889 345.938 560.928 18 18 453.433 0 34 1.949 0.030 2.441 0.060 2.728 99% -2 -1 0 p= Ex: 1.234 1 2 3 t = Ex: 1.234

Mean Variance Observations Pooled Variance Hypothesized Mean Difference df t Stat P[T<=t) one-tail t Critical one-tail P[T<=t) two-tail t Critical two-tail Confidence Level Southern Northern 155.056 168.889 345.938 560.928 18 18 453.433 0 34 1.949 0.030 2.441 0.060 2.728 99% -2 -1 0 p= Ex: 1.234 1 2 3 t = Ex: 1.234

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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