Form 90%, 95%, and 99% confidence intervals for the proportion of voters who favor the candidate. How do the intervals change as the level of confidence increases?

MATLAB: An Introduction with Applications
6th Edition
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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  1. In a survey regarding an upcoming presidential primary, 1000 people were asked whether or not they favor a particular candidate. 214 of the respondents indicated that they favor the candidate. Form 90%, 95%, and 99% confidence intervals for the proportion of voters who favor the candidate. How do the intervals change as the level of confidence increases?
**Question 3: Confidence Interval Analysis**

In a survey regarding an upcoming presidential primary, 1,000 people were asked whether or not they favor a particular candidate. Of those surveyed, 214 respondents indicated that they favor the candidate. Calculate the 90%, 95%, and 99% confidence intervals for the proportion of voters who favor the candidate. Discuss how the intervals change as the level of confidence increases.

**Explanation:**

This question explores the concept of confidence intervals in the context of a political survey. By determining the confidence intervals at different levels (90%, 95%, and 99%), we gain insight into how the precision and reliability of our estimate of the proportion may change with varying degrees of confidence. As the confidence level increases, the interval typically becomes wider, reflecting greater uncertainty required to maintain a higher certainty. 

Such an analysis is vital in understanding voter preferences and predicting electoral outcomes, ensuring a scientifically grounded interpretation of survey data.
Transcribed Image Text:**Question 3: Confidence Interval Analysis** In a survey regarding an upcoming presidential primary, 1,000 people were asked whether or not they favor a particular candidate. Of those surveyed, 214 respondents indicated that they favor the candidate. Calculate the 90%, 95%, and 99% confidence intervals for the proportion of voters who favor the candidate. Discuss how the intervals change as the level of confidence increases. **Explanation:** This question explores the concept of confidence intervals in the context of a political survey. By determining the confidence intervals at different levels (90%, 95%, and 99%), we gain insight into how the precision and reliability of our estimate of the proportion may change with varying degrees of confidence. As the confidence level increases, the interval typically becomes wider, reflecting greater uncertainty required to maintain a higher certainty. Such an analysis is vital in understanding voter preferences and predicting electoral outcomes, ensuring a scientifically grounded interpretation of survey data.
**Question 3: Confidence Intervals for Survey Results**

In a survey regarding an upcoming presidential primary, 1000 people were asked whether or not they favor a particular candidate. Out of these, 214 respondents indicated that they favor the candidate. Calculate the 90%, 95%, and 99% confidence intervals for the proportion of voters who favor the candidate. Discuss how these intervals change as the level of confidence increases.
Transcribed Image Text:**Question 3: Confidence Intervals for Survey Results** In a survey regarding an upcoming presidential primary, 1000 people were asked whether or not they favor a particular candidate. Out of these, 214 respondents indicated that they favor the candidate. Calculate the 90%, 95%, and 99% confidence intervals for the proportion of voters who favor the candidate. Discuss how these intervals change as the level of confidence increases.
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