**Survey Analysis and Confidence Interval Construction**When a recent survey asked subjects whether it should or should not be the government's responsibility to impose strict laws to make industry do less damage to the environment, 1407 of 1500 subjects said yes. Complete parts a and b below.**a. Assumptions for Constructing a 95% Confidence Interval**To construct a 95% confidence interval for the population proportion who would say yes, the following assumptions must be met:- The data must be obtained **randomly**.- The number of successes must be **at least 15**.- The number of failures must be **at least 15**.**Do the assumptions seem satisfied here?**- A. No, there are not enough or too many successes.- B. No, the data was not gathered properly.- C. No, there are not enough or too many failures.- D. ✔️ Yes, all assumptions seem satisfied.**b. Construction of the 95% Confidence Interval****Interpret in context:** Can you conclude whether or not a majority or minority of the population would answer yes?We can be **____%** confident that the interval **____ to ____** contains the population proportion who said yes.*(Type an integer or decimal rounded to three decimal places as needed.)*

Given that in a recent survey, 1407 of 1500 subjects said yes to the question it should or should not be the government's responsibility to impose strict laws to make industry do less damage to the environment. x=1407 and n=1500 p^=14071500=0.938 A 1001-α% confidence interval for the population proportion is p^±zα2p^1-p^n 1001-α%=95%1-α=0.95α=0.05α2=0.025 zα2=z0.025=z0.975=NORM.S.INV(0.975)=1.96 {using EXCEL} p^±zα2p^1-p^n=0.938±1.96×0.938×1-0.9381500=0.938±1.96×0.006227=0.938±0.012204=0.925796, 0.950204 Therefore, the 95% confidence interval is 0.926, 0.950. We can be 95% confident that the interval 0.926 to 0.950 contains the population proportion who said yes.

Math

Statistics

When a recent survey asked subjects whether it should or should not be the government's responsibility to impose strict laws to make industry do less damage to the environment, 1407 of 1500 subjects said yes. Complete parts a and b below. a. What assumptions are made to construct a 95% confidence interval for the population proportion who would say yes? Do they seem satisfied here? The data must be obtained randomly the number of successes must be at least 15, and the number of failures must be at least 15. Do the assumptions seem satisfied here? OA. No, there are not enough or too many successes. OB. No, the data was not gathered properly. O C. No, there are not enough or too many failures. D. Yes, all assumptions seem satisfied. b. Construct the 95% confidence interval. Interpret in context. Can you conclude whether or not a majority or minority of the population would answer yes? We can be confident that the interval to contains the population proportion who said yes. (Type an integer or decimal rounded to three decimal places as needed.)

When a recent survey asked subjects whether it should or should not be the government's responsibility to impose strict laws to make industry do less damage to the environment, 1407 of 1500 subjects said yes. Complete parts a and b below. a. What assumptions are made to construct a 95% confidence interval for the population proportion who would say yes? Do they seem satisfied here? The data must be obtained randomly the number of successes must be at least 15, and the number of failures must be at least 15. Do the assumptions seem satisfied here? OA. No, there are not enough or too many successes. OB. No, the data was not gathered properly. O C. No, there are not enough or too many failures. D. Yes, all assumptions seem satisfied. b. Construct the 95% confidence interval. Interpret in context. Can you conclude whether or not a majority or minority of the population would answer yes? We can be confident that the interval to contains the population proportion who said yes. (Type an integer or decimal rounded to three decimal places as needed.)

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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