Democracy and Free Press A 2017 survey of U.S. adults found the 64 % believed that freedom of news organization to criticize political leaders is essential to maintaining a strong democracy. Assume the sample size was 500. a. How many people in the sample felt this way? b. Is the sample large enough to apply the Central Limit Theorem? Explain. Assume all other conditions are met. c. Find a 95 % confidence interval for the proportion of U.S. adults who believe that freedom of news organizations to criticize political leaders is essential to maintaining a strong democracy. d. Find the width of the 95 % confidence interval. Round your answer to the nearest whole percent. e. Now assume the sample size was increased to 4500 and the percentage was still 64 % . Find a 95 % confidence interval and report the width of the interval. f. What happened to the width of the confidence interval when the sample size was increased. Did it increase or decrease?
Democracy and Free Press A 2017 survey of U.S. adults found the 64 % believed that freedom of news organization to criticize political leaders is essential to maintaining a strong democracy. Assume the sample size was 500. a. How many people in the sample felt this way? b. Is the sample large enough to apply the Central Limit Theorem? Explain. Assume all other conditions are met. c. Find a 95 % confidence interval for the proportion of U.S. adults who believe that freedom of news organizations to criticize political leaders is essential to maintaining a strong democracy. d. Find the width of the 95 % confidence interval. Round your answer to the nearest whole percent. e. Now assume the sample size was increased to 4500 and the percentage was still 64 % . Find a 95 % confidence interval and report the width of the interval. f. What happened to the width of the confidence interval when the sample size was increased. Did it increase or decrease?
Solution Summary: The author explains how the sample size is large enough to apply the Central Limit Theorem.
Democracy and Free Press A 2017 survey of U.S. adults found the
64
%
believed that freedom of news organization to criticize political leaders is essential to maintaining a strong democracy. Assume the sample size was 500.
a. How many people in the sample felt this way?
b. Is the sample large enough to apply the Central Limit Theorem? Explain. Assume all other conditions are met.
c. Find a
95
%
confidence interval for the proportion of U.S. adults who believe that freedom of news organizations to criticize political leaders is essential to maintaining a strong democracy.
d. Find the width of the
95
%
confidence interval. Round your answer to the nearest whole percent.
e. Now assume the sample size was increased to 4500 and the percentage was still
64
%
.
Find a
95
%
confidence interval and report the width of the interval.
f. What happened to the width of the confidence interval when the sample size was increased. Did it increase or decrease?
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
During busy political seasons, many opinion polls are conducted. In apresidential race, how do you think the participants in polls are generally selected?Discuss any issues regarding simple random, stratified, systematic, cluster, andconvenience sampling in these polls. What about other types of polls, besides political?
Please could you explain why 0.5 was added to each upper limpit of the intervals.Thanks
28. (a) Under what conditions do we say that two random variables X and Y are
independent?
(b) Demonstrate that if X and Y are independent, then it follows that E(XY) =
E(X)E(Y);
(e) Show by a counter example that the converse of (ii) is not necessarily true.
Elementary Statistics: Picturing the World (7th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.