Kierra V Hypothesis test for the difference of population proportions Español For several decades, it was a common practice in Southern California for houses to be built with pools in the backyard (as any airplane flight which ends at a Southern California airport will reveal). Now, however, that practice may be changing, possibly because of the recent demand for landscaped homes, which experts believe help reduce pollution. A recent study examined a random sample of 128 houses built in Southern California between 1950 and 1985 and an independent, random sample of 90 houses built in Southern California from 1992 to the present. The sample of houses built in 1950 - 1985 contained 51 houses with pools, and the sample of houses built from 1992 - present contained 21 houses with pools. Based on this survey, can we conclude, at the 0.05 level of significance, that the proportion p, of all Southern California houses built in 1950 - 1985 that were built with pools is greater than the proportion p, of all Southern California houses built from 1992 - present 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 hy.pothesis H, and the alternative hypothesis H,. H, :0 H :0 (b) Determine the type of test statistic to use. (Choose one) ▼ D=0 OSO (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.) (e) Can we conclude that the proportion of Southern California houses built with pools from 1950 - 1985 is greater than the proportion from 1985 - present? O Yes ONo olo
Kierra V Hypothesis test for the difference of population proportions Español For several decades, it was a common practice in Southern California for houses to be built with pools in the backyard (as any airplane flight which ends at a Southern California airport will reveal). Now, however, that practice may be changing, possibly because of the recent demand for landscaped homes, which experts believe help reduce pollution. A recent study examined a random sample of 128 houses built in Southern California between 1950 and 1985 and an independent, random sample of 90 houses built in Southern California from 1992 to the present. The sample of houses built in 1950 - 1985 contained 51 houses with pools, and the sample of houses built from 1992 - present contained 21 houses with pools. Based on this survey, can we conclude, at the 0.05 level of significance, that the proportion p, of all Southern California houses built in 1950 - 1985 that were built with pools is greater than the proportion p, of all Southern California houses built from 1992 - present 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 hy.pothesis H, and the alternative hypothesis H,. H, :0 H :0 (b) Determine the type of test statistic to use. (Choose one) ▼ D=0 OSO (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.) (e) Can we conclude that the proportion of Southern California houses built with pools from 1950 - 1985 is greater than the proportion from 1985 - present? O Yes ONo olo
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:### Hypothesis Test for the Difference of Population Proportions
#### Scenario:
For several decades, it was common in Southern California for homes to include pools in the backyard to help reduce pollution. A recent study examined two independent, random samples:
- 128 houses built between 1950 and 1985, with 51 houses having pools.
- 90 houses built from 1992 to the present, with 21 houses having pools.
The goal is to determine at the 0.05 level of significance if the proportion \( p_1 \) of houses from 1950–1985 with pools is greater than the proportion \( p_2 \) from 1992–present.
#### Instructions:
- Perform a **one-tailed test**.
#### Steps:
**(a) State the Hypotheses:**
- **Null Hypothesis \( H_0 \):** \( p_1 \leq p_2 \)
- **Alternative Hypothesis \( H_1 \):** \( p_1 > p_2 \)
**(b) Type of Test Statistic:**
- Choose the appropriate test statistic for comparing two proportions.
**(c) Calculate the Test Statistic:**
- Find and record the test statistic value, ensuring calculations are to three or more decimal places.
**(d) Find the p-Value:**
- Calculate the p-value and round to three or more decimal places.
**(e) Conclusion:**
- Determine if the data provides enough evidence to conclude that the proportion of houses with pools from 1950 to 1985 is greater than from 1992 to the present.
- Select "Yes" or "No" based on the p-value and level of significance.
#### Diagrams:
The interface includes a keypad for entering mathematical symbols and notations, including means (\( \mu \)), standard deviations (\( \sigma \)), and proportions (\( p \)), alongside options for various statistical measures.
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