Question

Three-circle, red-on-white is one distinctive pattern painted on ceramic vessels of the Anasazi period found at the Wind Mountain archaeological site. At one excavation, a sample of 176 potsherds indicated that 62 were of the three-circle, red-on-white pattern. How many ceramic potsherds must be found and identified if we are to be 95% confident that the sample proportion p̂ of such potsherds is within 5.0% of the population proportion of three-circle, red-on-white patterns found at this excavation site? (Round your answer up to the nearest whole number.)

Answer 1

Solution,

Given that,

n = 176

x = 62

$\hat p$ = x / n = 62 / 176 = 0.352

1 - $\hat p$ = 1 - 0.352 = 0.648

margin of error = E = 5.0% = 0.05

At 95% confidence level

$\alpha$ = 1 - 95%  

$\alpha$ = 1 - 0.95 =0.05

$\alpha$/2 = 0.025

Z$\alpha$/2 = Z_0.025 = 1.96

Sample size = n = (Z_{$\alpha$ / 2} / E )² * $\hat p$ * (1 - $\hat p$ )

= (1.96 / 0.05)² * 0.352 * 0.648

= 350.50

Sample size = n = 351