Question

Three-circle, red-on-white is one distinctive pattern painted on ceramic vessels of the Anasazi period found at an archaeological site. At one excavation, a sample of 177 potsherds indicated that 76 were of the three-circle, red-on-white pattern.

(a) Find a point estimate p̂ for the proportion of all ceramic potsherds at this site that are of the three-circle, red-on-white pattern. (Round your answer to four decimal places.)

(b) Compute a 95% confidence interval for the population proportion p of all ceramic potsherds with this distinctive pattern found at the site. (Round your answers to three decimal places.)

lower limit
upper limit

Answer 1

Solution :

Given that,

n = 177

x = 76

= x / n = 76 /177 = 0.4294 ( point estimate)

1 - = 1 - 0. 4294= 0.5706

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 * (((0.4294 * 0.5706) / 177) = 0.073

A 95 % confidence interval for population proportion p is ,

- E < P < + E

0.4294 - 0.073 < p < 0.4294+ 0.073

0.3564 < p < 0.5024

The 95% confidence interval for the population proportion p is :   lower limit = 0.3564

upper limit = 0.502