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 175 potsherds indicated that 66 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.)

Upper Limit:

Lower Limit:

Answer 1

Solution :

Given that,

n = 175

x = 66

= x / n = 66 / 175 = 0.377

1 - = 1 - 0.377 = 0.623

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 * (((0.377 * 0.623) / 175)

= 0..072

A 95% confidence interval for population proportion p is ,

- E < P < + E

0.377 - 0.072 < p < 0.377 + 0.072

0.305 < p < 0.449

Lower limit = 0.305

Uppetr limit = 0.449