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1- g Two different simple random samples are drawn from two different populations. The first sample consists of 40 people with 19 having a common attribute. The second sample consists with 1543 of them having the same common attribute. Compare the results from a hypothesis test of p₁=p₂ (with a 0.01 significance level) and a 99% confidence interval estimate of P₁-P2. Identify the test statistic. (Round to two decimal places as needed.) Identify the critical value(s); W (Round to three decimal places as needed. Use a comma to separate answers as needed) What is the conclusion based on the hypothesis test? The test statistic is the critical region, so the null hypothesis. There is EXIB evidence to conclude that p₁P2 people

1- g Two different simple random samples are drawn from two different populations. The first sample consists of 40 people with 19 having a common attribute. The second sample consists with 1543 of them having the same common attribute. Compare the results from a hypothesis test of p₁=p₂ (with a 0.01 significance level) and a 99% confidence interval estimate of P₁-P2. Identify the test statistic. (Round to two decimal places as needed.) Identify the critical value(s); W (Round to three decimal places as needed. Use a comma to separate answers as needed) What is the conclusion based on the hypothesis test? The test statistic is the critical region, so the null hypothesis. There is EXIB evidence to conclude that p₁P2 people

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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### Hypothesis Testing of Population Proportions Two different simple random samples are drawn from two different populations. The first sample consists of 40 people with 19 having a common attribute. The second sample consists of 2200 people with 1543 of them having the same common attribute. Compare the results from a hypothesis test of \( p_1 \neq p_2 \) (with a 0.01 significance level) and a 99% confidence interval estimate of \( p_1 - p_2 \). #### Steps in Hypothesis Testing 1. **Identify the Test Statistic:** - **Instruction**: Round to two decimal places as needed. - **Input box**: [ ] 2. **Identify the Critical Value(s):** - **Instruction**: Round to three decimal places as needed. Use a comma to separate answers as needed. - **Input box**: [ ] #### Conclusion Based on the Hypothesis Test - **Instruction**: Fill in the blanks to conclude: - The test statistic is [ ] the critical region, so [ ] the null hypothesis. There is [ ] evidence to conclude that \( p_1 \neq p_2 \). This process outlines how you can use statistical methods to compare proportions from two different samples and make meaningful conclusions based on the analysis.
Transcribed Image Text:### Hypothesis Testing of Population Proportions Two different simple random samples are drawn from two different populations. The first sample consists of 40 people with 19 having a common attribute. The second sample consists of 2200 people with 1543 of them having the same common attribute. Compare the results from a hypothesis test of \( p_1 \neq p_2 \) (with a 0.01 significance level) and a 99% confidence interval estimate of \( p_1 - p_2 \). #### Steps in Hypothesis Testing 1. **Identify the Test Statistic:** - **Instruction**: Round to two decimal places as needed. - **Input box**: [ ] 2. **Identify the Critical Value(s):** - **Instruction**: Round to three decimal places as needed. Use a comma to separate answers as needed. - **Input box**: [ ] #### Conclusion Based on the Hypothesis Test - **Instruction**: Fill in the blanks to conclude: - The test statistic is [ ] the critical region, so [ ] the null hypothesis. There is [ ] evidence to conclude that \( p_1 \neq p_2 \). This process outlines how you can use statistical methods to compare proportions from two different samples and make meaningful conclusions based on the analysis.
**Title: Testing Hypotheses with Confidence Intervals** **Introduction:** Two independent simple random samples are gathered from different populations. The first sample comprises 40 individuals, 19 of whom share a common attribute. The second sample comprises 2,200 individuals, with 1,543 possessing the same attribute. This content illustrates how to compare results from a hypothesis test of \( p_1 = p_2 \) (at a 0.01 significance level) with a 99% confidence interval estimate for \( p_1 - p_2 \). --- **Analysis:** 1. **Hypothesis Test Evaluation:** - The test statistic is compared to the critical region. - Based on this comparison, we determine whether to support or reject the null hypothesis. - Depending on the evidence, it may or may not be concluded that \( p_1 \neq p_2 \). 2. **Confidence Interval Calculation:** - The 99% confidence interval for the difference between the two population proportions is calculated and is given as: \(( \_ \_ , \_ \_ )\). - Values should be rounded to three decimal places as required. 3. **Conclusion from Confidence Interval:** - If zero lies within the confidence interval, it indicates potential support for the null hypothesis. - This presence (or absence) in the interval provides insight into the equivalence of the population proportions. 4. **Comparison of Methods:** - Results from the hypothesis test are compared with those from the confidence interval. - Conclusions about \( p_1 \) and \( p_2 \), whether the values suggest they are equal or different, are drawn from both approaches. --- By thoroughly analyzing the data through both hypothesis testing and confidence interval estimation, one can attain a comprehensive understanding of the relationship between two population proportions.
Transcribed Image Text:**Title: Testing Hypotheses with Confidence Intervals** **Introduction:** Two independent simple random samples are gathered from different populations. The first sample comprises 40 individuals, 19 of whom share a common attribute. The second sample comprises 2,200 individuals, with 1,543 possessing the same attribute. This content illustrates how to compare results from a hypothesis test of \( p_1 = p_2 \) (at a 0.01 significance level) with a 99% confidence interval estimate for \( p_1 - p_2 \). --- **Analysis:** 1. **Hypothesis Test Evaluation:** - The test statistic is compared to the critical region. - Based on this comparison, we determine whether to support or reject the null hypothesis. - Depending on the evidence, it may or may not be concluded that \( p_1 \neq p_2 \). 2. **Confidence Interval Calculation:** - The 99% confidence interval for the difference between the two population proportions is calculated and is given as: \(( \_ \_ , \_ \_ )\). - Values should be rounded to three decimal places as required. 3. **Conclusion from Confidence Interval:** - If zero lies within the confidence interval, it indicates potential support for the null hypothesis. - This presence (or absence) in the interval provides insight into the equivalence of the population proportions. 4. **Comparison of Methods:** - Results from the hypothesis test are compared with those from the confidence interval. - Conclusions about \( p_1 \) and \( p_2 \), whether the values suggest they are equal or different, are drawn from both approaches. --- By thoroughly analyzing the data through both hypothesis testing and confidence interval estimation, one can attain a comprehensive understanding of the relationship between two population proportions.
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