a The estimated standard error computes to b The 95 confide

(a) The estimated standard error computes to _________________?

(b) The 95% confidence interval is ________________?

(c) Suppose now the party is interested in a confidence interval at most .02 wide, with a confidence level of at least 95%. How large should the sample size n be?

Solution

a) Proportion of people who intend to vote for a ceryain party p = 41/100 = 0.41

N = 100

Std Error = sqrt(p (1 - p)/n) = sqrt(0.41 * (1 - 0.41)/100) = 0.05

b) alpha = 0.05

critical value for alpha 0.05 is + 1.96

Margin of Error = Crit value * Std error = + 1.96 * 0.05 = + 0.096

Confidence interval = 0.41 + 0.096 = (0.314 , 0.507)

c) Width of confidence interval = 0.02

Margin of error = 0.02/2 = 0.01

0.01 = + 1.96 * sqrt(0.41 * (1 - 0.41)/n)

n = 9,293