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 78 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 = 78

Point estimate = sample proportion = = x / n = 78/173=0.4509

1 -   = 1- 0.4509 =0.5491

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

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

= 1.96 (((0.4509*0.5491) / 173)

E = 0.074

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.4509-0.074 < p <0.4509+ 0.074

0.377< p < 0.525

The 95% confidence interval for the population proportion p is : lower limit=0.377,upper limit= 0.525