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 178 potsherds indicated that 70 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 5.7% 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 = 178

x = 70

Point estimate = sample proportion = = x / n = 70 / 178 = 0.39

1 - = 1 - 0.39 = 0.61

margin of error = E = 0.057

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025  = 1.96

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

= (1.96 / 0.057)2 * 0.39 *0.61

= 281.29

sample size = n = 282  ceramic potsherds