In a survey of 2003 adults in a recent year, 737 made a New Year's resolution to eat healthier. Construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. .... The 90% confidence interval for the population proportion p is ( ID (Round to three decimal places as needed.) The 95% confidence interval for the population proportion p is ( D (Round to three decimal places as needed.) With the given confidence, it can be said that the population proportion of adults who say they have made a New Year's resolution to eat healthier is between the endpoints of the given confidence interval. Compare the widths of the confidence intervals. Choose the correct answer below. O A. The 90% confidence interval is wider. O B. The 95% confidence interval is wider. O C. The confidence intervals cannot be compared. The confidence intervals are the same width.
In a survey of 2003 adults in a recent year, 737 made a New Year's resolution to eat healthier. Construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. .... The 90% confidence interval for the population proportion p is ( ID (Round to three decimal places as needed.) The 95% confidence interval for the population proportion p is ( D (Round to three decimal places as needed.) With the given confidence, it can be said that the population proportion of adults who say they have made a New Year's resolution to eat healthier is between the endpoints of the given confidence interval. Compare the widths of the confidence intervals. Choose the correct answer below. O A. The 90% confidence interval is wider. O B. The 95% confidence interval is wider. O C. The confidence intervals cannot be compared. The confidence intervals are the same width.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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![**Title: Exploring Confidence Intervals in Survey Data**
**Introduction**
In a survey of 2003 adults conducted in a recent year, 737 individuals reported having made a New Year's resolution to eat healthier. This study aims to construct 90% and 95% confidence intervals for the population proportion, interpret the results, and compare the widths of the confidence intervals.
**Confidence Interval Construction**
1. **90% Confidence Interval:**
- The 90% confidence interval for the population proportion \( p \) is **( [Input required] )**.
- *Instructions*: Round your answers to three decimal places as needed.
2. **95% Confidence Interval:**
- The 95% confidence interval for the population proportion \( p \) is **( [Input required] )**.
- *Instructions*: Round your answers to three decimal places as needed.
**Interpretation**
- With the given confidence level, it can be asserted that the population proportion of adults who say they have made a New Year's resolution to eat healthier is **between the endpoints** of the given confidence interval.
**Comparison of Confidence Intervals**
- We are tasked with comparing the widths of the confidence intervals.
**Options for Comparison:**
- **A.** The 90% confidence interval is wider.
- **B.** The 95% confidence interval is wider.
- **C.** The confidence intervals cannot be compared.
- **D.** The confidence intervals are the same width.
*Note: Typically, a 95% confidence interval is expected to be wider than a 90% confidence interval because it provides a higher level of confidence, encompassing more variability.*
**Conclusion**
Click **Next** to proceed with calculating and interpreting the results based on the methods outlined above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02fc7836-9552-4a6b-92e4-0fb932880b81%2Fa032efc4-6e74-478e-b77c-27259ff88309%2F5vdgk5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Exploring Confidence Intervals in Survey Data**
**Introduction**
In a survey of 2003 adults conducted in a recent year, 737 individuals reported having made a New Year's resolution to eat healthier. This study aims to construct 90% and 95% confidence intervals for the population proportion, interpret the results, and compare the widths of the confidence intervals.
**Confidence Interval Construction**
1. **90% Confidence Interval:**
- The 90% confidence interval for the population proportion \( p \) is **( [Input required] )**.
- *Instructions*: Round your answers to three decimal places as needed.
2. **95% Confidence Interval:**
- The 95% confidence interval for the population proportion \( p \) is **( [Input required] )**.
- *Instructions*: Round your answers to three decimal places as needed.
**Interpretation**
- With the given confidence level, it can be asserted that the population proportion of adults who say they have made a New Year's resolution to eat healthier is **between the endpoints** of the given confidence interval.
**Comparison of Confidence Intervals**
- We are tasked with comparing the widths of the confidence intervals.
**Options for Comparison:**
- **A.** The 90% confidence interval is wider.
- **B.** The 95% confidence interval is wider.
- **C.** The confidence intervals cannot be compared.
- **D.** The confidence intervals are the same width.
*Note: Typically, a 95% confidence interval is expected to be wider than a 90% confidence interval because it provides a higher level of confidence, encompassing more variability.*
**Conclusion**
Click **Next** to proceed with calculating and interpreting the results based on the methods outlined above.
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