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 173 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 = 173

x = 76

Point Estimate () = x / n = 0.439

1 - = 1 - 0.439 = 0.561

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 * [(0.439 * 0.561) / 173]

= 0.074

A 95% confidence interval for population proportion p is ,

- E < P < + E

0.439 - 0.074 < p < 0.439 + 0.074

0.365 < p < 0.513

Lower Limit = 0.365

Upper Limit = 0.513