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 64 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,

(a)

Point estimate = sample proportion = = x / n = 64 / 175 = 0.3657

(b)

Z_/2 = 1.96

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

= 1.645 * (((0.3657 * 0.6343) / 175)

= 0.072

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.3657 - 0.072 < p < 0.3657 + 0.072

0.294 < p < 0.438

Lower limit =0.294

Upper limit = 0.438