Question

A medical researcher wishes to determine the percentage of females who take vitamins. He wishes to be 95% confident that the estimate is within 5 percentage points of the true proportion. A recent study of 320 females showed that 45% took vitamins. How large should the sample size be?

		380
		381
		9
		10

Answer 1

Solution :

Given that,

= 0.45

1 - = 0.55

margin of error = E = 0.05

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.96 / 0.05)2 * 0.45 * 0.55

= 380.32

sample size = 381