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 181 potsherds indicated that 66were 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,

(a)

Point estimate = sample proportion = = x / n = 66 / 181 = 0.3646

1 - = 1 - 0.3646 = 0.6354

Z/2 = 1.96

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

= 1.96 * (((0.3646 * 0.6346) / 181)

Margin of error = E = 0.070

(b)

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.3646 - 0.070 < p < 0.3646 + 0.070

0.295 < p < 0.435

Lower limit: 0.295

Upper limit: 0.435