Question

*ANSWER USING R-SCRIPT*

We desire to know the probability that a voter supports a controversial rose proposal. From a random sample of 3100, x =1331 voters support the rose proposal. Let phat be the sample proportion supporting the rose proposal. Answer the following:

a) what is the variance of p hat

b) As a function of p, what is the standard deviation of p hat

c) Calculate p hat

d) Let ptot be the random variable representing the voters in the sample who support the rose proposal. As a function of p, what is the standard deviation of ptot?

e) Calculate a classical 96% confidence interval for p

f) What is the critical value for an approximate classical 94 percent confidence interval for p?

g) What is the length of the 96% confidence interval for p?

h) Assuming the same phat value, what sample size would have made the 96% confidence interval for p to have a length of .08 or less?

Answer 1

>N-3100 > x-1331 > phat=x/N > ## PART-A > var phat-phat (1-phat)/N > var phat [1] 7.903525e-05 > ## PART-B > stdev_phat-sqrt (phat (1-phat)/N) > stdev phat [1] 0.008890177 > ## PART-C > phat [1] 0.4293548 > ## PART-D > 3tdev_ptot=sqrt (N-phat* (1-phat) ) > stdev ptot [1] 27.55955