### Analyzing the Prevalence of Pools in Southern California HomesIn the twentieth century, it was common in Southern California for homes to be built with pools in the backyard. Recently, there has been a change due to potential climate impact reduction efforts. A study examined a random sample of 144 houses built in the twentieth century and a sample of 67 recent new houses in Southern California. The twentieth-century sample had 71 houses with pools, while the new sample had 20 houses with pools.**Objective:** Determine if the proportion \( p_1 \) of all Southern California twentieth-century houses with pools is greater than the proportion \( p_2 \) of all new Southern California houses with pools using a one-tailed test at a 0.05 level of significance.#### Steps for Analysis1. **Hypotheses Setup** - **Null Hypothesis** \( H_0 \): The proportion of houses with pools in the twentieth-century sample is equal to or less than in the new house sample. - **Alternative Hypothesis** \( H_1 \): The proportion of twentieth-century houses with pools is greater than the new house sample.2. **Type of Test Statistic** - Choose the appropriate test statistic, likely a Z-test due to proportions being involved.3. **Calculate the Test Statistic** - Perform calculations to determine the test statistic value. Round to three or more decimal places.4. **Determine the Critical Value** - Identify the critical value at a 0.05 level of significance, rounding to three or more decimal places.5. **Table and Symbols** - The table shown in the image allows selection and insertion of statistical symbols necessary for hypothesis statements and calculations.6. **Conclusion** - Based on the comparison of the test statistic to the critical value, conclude whether to reject or fail to reject the null hypothesis.**Note:** For detailed calculations, intermediate computations should be carried to three or more decimal places. Consult relevant statistical formulas as necessary.---**Resources:** For additional assistance, refer to statistical texts or online resources that discuss hypothesis testing, specifically concerning proportions. The image is a section of a webpage titled "Hypothesis test for the difference of population proportions". It guides users through a hypothesis test, prompting them to input their answers in the form provided. Let's go through each step in detail:### Sections:1. **Hypothesis Statements**: - **Null Hypothesis (\(H_0\))**: Enter your statement here about the populations being equal. - **Alternative Hypothesis (\(H_1\))**: Enter the hypothesis statement about the populations not being equal. 2. **Test Statistic**: - **Determine the Type**: Use the dropdown menu to choose the appropriate test statistic for the hypothesis test.3. **Value of the Test Statistic**: - **Calculation Field**: Input the calculated test statistic value. Users are instructed to round to three or more decimal places.4. **Critical Value**: - **Significance Level**: Find and enter the critical value corresponding to a 0.05 level of significance.5. **Conclusion**: - **Comparison of Proportions**: Answer whether the proportion of Southern California twentieth-century houses with pools is greater than the proportion for new homes. Options provided are 'Yes' or 'No'.### Tools Displayed:- **Symbols and Operators**: There are various mathematical symbols provided on the right side for easy input, including: - Greek letters (e.g., \(\mu, \sigma, \rho\)) - Mathematical operators and symbols like standard deviation \(s\) and proportions \(\hat{p}\).This section is part of an interactive online educational platform (© 2022 McGraw Hill LLC) where users can test their understanding of statistical tests with step-by-step input fields and explanations.

For twentieth-century houses: The sample size The houses with pools For new houses: The sample size…

75°F Cloudy In the twentieth century, it was a common practice in Southern California for houses to be built with pools in the backyard. For new homes, howeve practice may be changing, possibly as a measure to help reduce climate change. A recent study examined a random sample of 144 houses built in California in the twentieth century and an independent, random sample of 67 new houses built in Southern California. The sample of twentieth cent contained 71 houses with pools, and the sample of new houses contained 20 houses with pools. Based on this survey, can we conclude, at the 0.05 level of significance, that the proportion p₁ of all Southern California twentieth century houses t with pools is greater than the proportionh p, of all new Southern California houses that were built with pools? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the parts below. (If necessary, consul formulas.) (a) State the null hypothesis H, and the alternative hypothesis H₁. Ho :O H₁ :0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the critical value at the 0.05 level of sianificance. (Round to three or more decimal places.). Explanation Check FULL HD 144Hz ‒‒ - O Search H x ローロ X O S Do OSO O © 2022 McGraw Hill LLC. All Rights Reserved. Tem

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P