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A researcher wishes to estimate, with 90% confidence, the population proportion of adults who think Congress is doing a good or excellent job. Her estimate must be accurate within 5% of the true proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that 40% of the respondents said they think Congress is doing a good or excellent job. (c) Compare the results from parts (a) and (b). ....... (a) What is the minimum sample size needed assuming that no prior information is available? n= 271 (Round up to the nearest whole number as needed.) (b) What is the minimum sample size needed using a prior study that found that 40% of the respondents said they think Congress is doing a good or excellent job? n= 260 (Round up to the nearest whole number as needed.) (c) How do the results from (a) and (b) compare? O A. Having an estimate of the population proportion has no effect on the minimum sample size needed. O B. Having an estimate of the population proportion raises the minimum sample size needed. O C. Having an estimate of the population proportion reduces the minimum sample size needed.

A researcher wishes to estimate, with 90% confidence, the population proportion of adults who think Congress is doing a good or excellent job. Her estimate must be accurate within 5% of the true proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that 40% of the respondents said they think Congress is doing a good or excellent job. (c) Compare the results from parts (a) and (b). ....... (a) What is the minimum sample size needed assuming that no prior information is available? n= 271 (Round up to the nearest whole number as needed.) (b) What is the minimum sample size needed using a prior study that found that 40% of the respondents said they think Congress is doing a good or excellent job? n= 260 (Round up to the nearest whole number as needed.) (c) How do the results from (a) and (b) compare? O A. Having an estimate of the population proportion has no effect on the minimum sample size needed. O B. Having an estimate of the population proportion raises the minimum sample size needed. O C. Having an estimate of the population proportion reduces the minimum sample size needed.

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: Estimating Population Proportion with Confidence** A researcher aims to estimate, with 90% confidence, the population proportion of adults who believe Congress is doing a good or excellent job. The estimate must be accurate within 5% of the true proportion. 1. **No Preliminary Estimate Available** - Find the minimum sample size required. - Calculated Sample Size: \( n = 271 \) (Round up to the nearest whole number as needed.) 2. **Using a Prior Study Estimate** - A prior study indicates that 40% of respondents think Congress is doing a good or excellent job. - Calculated Sample Size: \( n = 260 \) (Round up to the nearest whole number as needed.) 3. **Comparison of Results** - How do the results from the first and second estimates compare? **Options:** - A: Having an estimate of the population proportion has no effect on the minimum sample size needed. - B: Having an estimate of the population proportion raises the minimum sample size needed. - C: Having an estimate of the population proportion reduces the minimum sample size needed. **Conclusion:** - This exercise demonstrates how having prior knowledge about the population proportion can potentially reduce the sample size required for achieving a specified confidence level and margin of error in statistical estimates.
Transcribed Image Text:**Title: Estimating Population Proportion with Confidence** A researcher aims to estimate, with 90% confidence, the population proportion of adults who believe Congress is doing a good or excellent job. The estimate must be accurate within 5% of the true proportion. 1. **No Preliminary Estimate Available** - Find the minimum sample size required. - Calculated Sample Size: \( n = 271 \) (Round up to the nearest whole number as needed.) 2. **Using a Prior Study Estimate** - A prior study indicates that 40% of respondents think Congress is doing a good or excellent job. - Calculated Sample Size: \( n = 260 \) (Round up to the nearest whole number as needed.) 3. **Comparison of Results** - How do the results from the first and second estimates compare? **Options:** - A: Having an estimate of the population proportion has no effect on the minimum sample size needed. - B: Having an estimate of the population proportion raises the minimum sample size needed. - C: Having an estimate of the population proportion reduces the minimum sample size needed. **Conclusion:** - This exercise demonstrates how having prior knowledge about the population proportion can potentially reduce the sample size required for achieving a specified confidence level and margin of error in statistical estimates.
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