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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)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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.
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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