Question

A private opinion poll is conducted for a politician to determine what proportion of the population favors decriminalizing marijuana possession. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 2%?

A. 2401

B. 25

C. 1692

D. 4802

Answer 1

Solution:

Given:

c = confidence level = 95%

E = Margin of Error = 2% = 0.02

Since p is unknown , we use p = 0.5

Formula for sample size n is:

We need to find z_c value for c=95% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750

Look in z table for Area = 0.9750 or its closest area and find z value.

Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96

That is : Z_c = 1.96

Thus

Thus correct option is A. 2401