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Constructing a Confidence Interval for the Population Proportion The Berkman center for Internet and Society at Harvard recently conducted a study analyzing the privacy management habits of teen Internet users. In a group of 50 teens, 13 reported having more than 500 friends on Facebook. Use the "plus four" method to find a 90% confidence interval for the true proportion of teens who would report having more than 500 Facebook friends. Work toward the required confidence interval by providing the information below. Confidence Level Area in One Tail Z-Score 50% 0.25 0.674 80% 0.1 1.282 90% 0.05 1.645 95% 0.025 1.96 98% 0.1 2.326 99% 0.005 2.576 (Include three decimal places below) а. р' b. a = C. 20.05 =

Constructing a Confidence Interval for the Population Proportion The Berkman center for Internet and Society at Harvard recently conducted a study analyzing the privacy management habits of teen Internet users. In a group of 50 teens, 13 reported having more than 500 friends on Facebook. Use the "plus four" method to find a 90% confidence interval for the true proportion of teens who would report having more than 500 Facebook friends. Work toward the required confidence interval by providing the information below. Confidence Level Area in One Tail Z-Score 50% 0.25 0.674 80% 0.1 1.282 90% 0.05 1.645 95% 0.025 1.96 98% 0.1 2.326 99% 0.005 2.576 (Include three decimal places below) а. р' b. a = C. 20.05 =

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
Problem 1P
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**Constructing a Confidence Interval for the Population Proportion** The Berkman Center for Internet and Society at Harvard recently conducted a study analyzing the privacy management habits of teen Internet users. In a group of 50 teens, 13 reported having more than 500 friends on Facebook. Use the "plus four" method to find a 90% confidence interval for the true proportion of teens who would report having more than 500 Facebook friends. Work toward the required confidence interval by providing the information below. **Table: Confidence Levels and Corresponding Z-Scores** | **Confidence Level** | **Area in One Tail** | **Z-Score** | |----------------------|----------------------|-------------| | 50% | 0.25 | 0.674 | | 80% | 0.1 | 1.282 | | 90% | 0.05 | 1.645 | | 95% | 0.025 | 1.96 | | 98% | 0.01 | 2.326 | | 99% | 0.005 | 2.576 | **Instructions:** (Include three decimal places below) a. \( p' = \) [_______________] b. \( \alpha = \) [_______________] c. \( z_{0.05} = \) [_______________] d. EBP (Estimated Binomial Proportion) = [_______________] e. We are 90% confident that the true proportion is above [________________] f. We are 90% confident that the true proportion is below [________________] g. Suppose the researchers from the previous problem wanted to reduce their EBP by 50%. What sample size would be needed? Assume \( p' \) is the same. \( n = \) [_____________] (Round to the nearest whole number)
Transcribed Image Text:**Constructing a Confidence Interval for the Population Proportion** The Berkman Center for Internet and Society at Harvard recently conducted a study analyzing the privacy management habits of teen Internet users. In a group of 50 teens, 13 reported having more than 500 friends on Facebook. Use the "plus four" method to find a 90% confidence interval for the true proportion of teens who would report having more than 500 Facebook friends. Work toward the required confidence interval by providing the information below. **Table: Confidence Levels and Corresponding Z-Scores** | **Confidence Level** | **Area in One Tail** | **Z-Score** | |----------------------|----------------------|-------------| | 50% | 0.25 | 0.674 | | 80% | 0.1 | 1.282 | | 90% | 0.05 | 1.645 | | 95% | 0.025 | 1.96 | | 98% | 0.01 | 2.326 | | 99% | 0.005 | 2.576 | **Instructions:** (Include three decimal places below) a. \( p' = \) [_______________] b. \( \alpha = \) [_______________] c. \( z_{0.05} = \) [_______________] d. EBP (Estimated Binomial Proportion) = [_______________] e. We are 90% confident that the true proportion is above [________________] f. We are 90% confident that the true proportion is below [________________] g. Suppose the researchers from the previous problem wanted to reduce their EBP by 50%. What sample size would be needed? Assume \( p' \) is the same. \( n = \) [_____________] (Round to the nearest whole number)
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