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Perform a chi-square independence test, provided the conditions for using the test are met. Researchers studied the bone mineral density (BMD) and depression of men aged 65 to 92 years. At the 1% significance level, do the data in the table (taken from a random sample) provide sufficient evidence to conclude that BMD and depression are statistically dependent for elderly men? E Click on the icon to view the data table. .AARD What are the null and alternative hypotheses? O A. H: Depression and BMD in elderly men are statistically dependent. H Depression and BMD in elderly men are statistically independent. O B. Ho: Depression and BMD in elderly men are statistically independent. H: Depression and BMD in elderly men are statistically dependent. O C. Ho: BMD is dependent upon depression in elderly men. Hg: Depression is dependent upon BMD in elderly men. Find the test statistic. xx = (Round to three decimal places as needed.) Find the P-value. P= (Round to four decimal places as needed.) What is the conclusion of the in V Ho. The data Data Table Depressed Not depressed Total Osteoporotic Low BMD Normal Total 4 34 38 72 532 604 95 1253 1348 171 1819 1990 Print Done

Perform a chi-square independence test, provided the conditions for using the test are met. Researchers studied the bone mineral density (BMD) and depression of men aged 65 to 92 years. At the 1% significance level, do the data in the table (taken from a random sample) provide sufficient evidence to conclude that BMD and depression are statistically dependent for elderly men? E Click on the icon to view the data table. .AARD What are the null and alternative hypotheses? O A. H: Depression and BMD in elderly men are statistically dependent. H Depression and BMD in elderly men are statistically independent. O B. Ho: Depression and BMD in elderly men are statistically independent. H: Depression and BMD in elderly men are statistically dependent. O C. Ho: BMD is dependent upon depression in elderly men. Hg: Depression is dependent upon BMD in elderly men. Find the test statistic. xx = (Round to three decimal places as needed.) Find the P-value. P= (Round to four decimal places as needed.) What is the conclusion of the in V Ho. The data Data Table Depressed Not depressed Total Osteoporotic Low BMD Normal Total 4 34 38 72 532 604 95 1253 1348 171 1819 1990 Print Done

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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**Chi-Square Independence Test: Conditions and Analysis** **Context:** Researchers studied the relationship between bone mineral density (BMD) and depression in men aged 65 to 92 years. At a 1% significance level, the objective is to determine if the data provides sufficient evidence to conclude that BMD and depression are statistically dependent for elderly men. **Hypotheses:** - **Option A:** - \( H_0 \): Depression and BMD in elderly men are statistically dependent. - \( H_a \): Depression and BMD in elderly men are statistically independent. - **Option B:** - \( H_0 \): Depression and BMD in elderly men are statistically independent. - \( H_a \): Depression and BMD in elderly men are statistically dependent. - **Option C:** - \( H_0 \): BMD is dependent upon depression in elderly men. - \( H_a \): Depression is dependent upon BMD in elderly men. **Data Table:** | BMD Classification | Depressed | Not Depressed | Total | |---------------------|------------|----------------|-------| | Osteoporotic | 4 | 34 | 38 | | Low BMD | 72 | 532 | 604 | | Normal | 95 | 1253 | 1348 | | **Total** | 171 | 1819 | 1990 | **Analysis:** 1. **Calculate the Chi-Square Test Statistic (\(\chi^2\)):** - Round to three decimal places as needed. 2. **P-Value Calculation:** - Round to four decimal places as needed. **Conclusion:** - Select the correct hypothesis based on the test statistic and the P-value at the 1% significance level. Determine whether to reject or fail to reject \( H_0 \). This analysis helps explore if a statistical dependency exists between BMD and depression in the specified demographic.
Transcribed Image Text:**Chi-Square Independence Test: Conditions and Analysis** **Context:** Researchers studied the relationship between bone mineral density (BMD) and depression in men aged 65 to 92 years. At a 1% significance level, the objective is to determine if the data provides sufficient evidence to conclude that BMD and depression are statistically dependent for elderly men. **Hypotheses:** - **Option A:** - \( H_0 \): Depression and BMD in elderly men are statistically dependent. - \( H_a \): Depression and BMD in elderly men are statistically independent. - **Option B:** - \( H_0 \): Depression and BMD in elderly men are statistically independent. - \( H_a \): Depression and BMD in elderly men are statistically dependent. - **Option C:** - \( H_0 \): BMD is dependent upon depression in elderly men. - \( H_a \): Depression is dependent upon BMD in elderly men. **Data Table:** | BMD Classification | Depressed | Not Depressed | Total | |---------------------|------------|----------------|-------| | Osteoporotic | 4 | 34 | 38 | | Low BMD | 72 | 532 | 604 | | Normal | 95 | 1253 | 1348 | | **Total** | 171 | 1819 | 1990 | **Analysis:** 1. **Calculate the Chi-Square Test Statistic (\(\chi^2\)):** - Round to three decimal places as needed. 2. **P-Value Calculation:** - Round to four decimal places as needed. **Conclusion:** - Select the correct hypothesis based on the test statistic and the P-value at the 1% significance level. Determine whether to reject or fail to reject \( H_0 \). This analysis helps explore if a statistical dependency exists between BMD and depression in the specified demographic.
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