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, however, that practice may be changing, possibly as a measure to help reduce climate change. A recent study examined a random sample of 135 houses built in Southern California in the twentieth century and an independent, random sample of 95 new houses built in Southern California. The sample of twentieth century houses contained 52 houses with pools, and the sample of new houses contained 33 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 that were built with pools is greater than the proportion p₂ 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, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H₁. H:0 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.) (d) Find the p-value. (Round to three or more decimal places.) Explanation Check 3. Ix X a 9 8 D S O=O OSO X OO 4 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use Priv
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, however, that practice may be changing, possibly as a measure to help reduce climate change. A recent study examined a random sample of 135 houses built in Southern California in the twentieth century and an independent, random sample of 95 new houses built in Southern California. The sample of twentieth century houses contained 52 houses with pools, and the sample of new houses contained 33 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 that were built with pools is greater than the proportion p₂ 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, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H₁. H:0 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.) (d) Find the p-value. (Round to three or more decimal places.) Explanation Check 3. Ix X a 9 8 D S O=O OSO X OO 4 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use Priv
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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Transcribed Image Text: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, however, that practice may be changing, possibly as a measure to help reduce climate change. A recent study examined a random sample of 135 houses built in Southern California in the twentieth century and an independent, random sample of 95 new houses built in Southern California. The sample of twentieth-century houses contained 52 houses with pools, and the sample of new houses contained 33 houses with pools.
Based on this survey, can we conclude, at the 0.05 level of significance, that the proportion \( P_1 \) of all Southern California twentieth-century houses that were built with pools is greater than the proportion \( P_2 \) 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, consult a list of formulas.)
(a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \).
\( H_0 \) : □
\( H_1 \) : □
(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.)
□
(d) Find the p-value. (Round to three or more decimal places.)
□
Explanation | Check
---
On the right side of the image, there's a tool for entering mathematical symbols and expressions, including options for means, proportions, various operators, and test statistics.
![**Hypothesis Testing Exercise**
This exercise guides you through performing hypothesis testing about proportions. Follow the steps below to complete the hypothesis test based on Southern California twentieth-century house data.
---
**Instructions:**
**(a) State the Hypotheses**
- **Null Hypothesis (\(H_0\))**:
\( \)
- **Alternative Hypothesis (\(H_1\))**:
\( \)
**(b) Determine the Type of Test Statistic to Use**
- Select the appropriate statistical test from the options provided to analyze the hypotheses.
**(c) Calculate the Test Statistic**
- Compute the test statistic. Ensure that you round your answer to three or more decimal places. Enter your result in the space provided.
**(d) Find the p-Value**
- Calculate the p-value rounding to three or more decimal places. Enter the result in the designated space.
**(e) Conclusion**
Evaluate the results:
- Can we conclude that the proportion of Southern California twentieth-century houses built with pools is greater than the proportion for new homes?
- [ ] Yes
- [ ] No
---
**Toolbox Key:**
The image includes symbols for statistical notation, used to input and format mathematical expressions:
- \(\mu\), \(\sigma\), \(p\): symbols for mean, standard deviation, and proportion respectively.
- \(\bar{x}\), \(s\), \(\hat{p}\): symbols representing sample mean, sample standard deviation, and sample proportion.
- Various square and circle icons are likely for selecting or formatting data input.
This exercise is designed to test understanding of hypothesis testing procedures and statistical analysis in the context of real estate data.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab310076-c445-4f02-aa72-05faca788dac%2F9c61a447-864c-4a15-b190-bd76b364f375%2Ff114jul_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Hypothesis Testing Exercise**
This exercise guides you through performing hypothesis testing about proportions. Follow the steps below to complete the hypothesis test based on Southern California twentieth-century house data.
---
**Instructions:**
**(a) State the Hypotheses**
- **Null Hypothesis (\(H_0\))**:
\( \)
- **Alternative Hypothesis (\(H_1\))**:
\( \)
**(b) Determine the Type of Test Statistic to Use**
- Select the appropriate statistical test from the options provided to analyze the hypotheses.
**(c) Calculate the Test Statistic**
- Compute the test statistic. Ensure that you round your answer to three or more decimal places. Enter your result in the space provided.
**(d) Find the p-Value**
- Calculate the p-value rounding to three or more decimal places. Enter the result in the designated space.
**(e) Conclusion**
Evaluate the results:
- Can we conclude that the proportion of Southern California twentieth-century houses built with pools is greater than the proportion for new homes?
- [ ] Yes
- [ ] No
---
**Toolbox Key:**
The image includes symbols for statistical notation, used to input and format mathematical expressions:
- \(\mu\), \(\sigma\), \(p\): symbols for mean, standard deviation, and proportion respectively.
- \(\bar{x}\), \(s\), \(\hat{p}\): symbols representing sample mean, sample standard deviation, and sample proportion.
- Various square and circle icons are likely for selecting or formatting data input.
This exercise is designed to test understanding of hypothesis testing procedures and statistical analysis in the context of real estate data.
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