We wish to determine the unknown probability p, that a voter
supports the controversial tulip proposal. We wish to estimate p.
We take a random sample of n=3100 voters. x=1331 of these voters
support the tulip proposal. Let p̂ be the sample proportion of
voters supporting the tulip proposal. Answer the following
using R code.
a)As a function of p, what is the variance of p̂? (use R
code)
b) As a function of p, what is the standard deviation of p̂?
(use R code)
d) Let ptot be the random variable representing the total number
of voters in the sample who support the tulip proposal. As a
function of p, what is the standard deviation of ptot?(use
R code)
h) Assuming the same p̂ value, what sample size would have made
the 93% confidence interval for p have a length of .08 or
less?(use R code)
