Local TV News Pew Research reported that 46 % of Americans surveyed in 2016 got their news from local television. A similar survey conducted in 2017 found that 37 % of Americans got their news from local television. Assume the sample size for each poll was 1200. a. Construct the 95 % confidence interval for the difference in the proportions of Americans who get their news from local television in 2016 and 2017. b. Based on your interval, do you think there has been a change in the pro-portion of Americans who get their news from local television? Explain.
Local TV News Pew Research reported that 46 % of Americans surveyed in 2016 got their news from local television. A similar survey conducted in 2017 found that 37 % of Americans got their news from local television. Assume the sample size for each poll was 1200. a. Construct the 95 % confidence interval for the difference in the proportions of Americans who get their news from local television in 2016 and 2017. b. Based on your interval, do you think there has been a change in the pro-portion of Americans who get their news from local television? Explain.
Solution Summary: The author calculates the confidence interval for the difference in the proportion of Americans who got their news from local news in 2016 and 2017. The sample size of each poll is 1200.
Local TV News Pew Research reported that
46
%
of Americans surveyed in 2016 got their news from local television. A similar survey conducted in 2017 found that
37
%
of Americans got their news from local television. Assume the sample size for each poll was 1200.
a. Construct the
95
%
confidence interval for the difference in the proportions of Americans who get their news from local television in 2016 and 2017.
b. Based on your interval, do you think there has been a change in the pro-portion of Americans who get their news from local television? Explain.
Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.
A random variable X takes values 0 and 1 with probabilities q and p, respectively, with q+p=1. find the moment generating function of X and show that all the moments about the origin equal p. (Note- Please include as much detailed solution/steps in the solution to understand, Thank you!)
1 (Expected Shortfall)
Suppose the price of an asset Pt follows a normal random walk, i.e., Pt =
Po+r₁ + ... + rt with r₁, r2,... being IID N(μ, o²).
Po+r1+.
⚫ Suppose the VaR of rt is VaRq(rt) at level q, find the VaR of the price
in T days, i.e., VaRq(Pt – Pt–T).
-
• If ESq(rt) = A, find ES₁(Pt – Pt–T).
2 (Normal Distribution)
Let rt be a log return. Suppose that r₁, 2, ... are IID N(0.06, 0.47).
What is the distribution of rt (4) = rt + rt-1 + rt-2 + rt-3?
What is P(rt (4) < 2)?
What is the covariance between r2(2) = 1 + 12 and 13(2) = r² + 13?
• What is the conditional distribution of r₁(3) = rt + rt-1 + rt-2 given
rt-2 = 0.6?
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