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 80 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 = 181

x = 80

Point estimate = sample proportion = = x / n =80/181=0.4420

1 -   = 1- 0.4420 =0.5580

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 (((0.4420*0.5580) /181 )

E = 0.072

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.4420-0.072 < p <0.4420+ 0.072

0.370< p <0.514

The 95% confidence interval for the population proportion p is : lower limit=0.370,upper limit=0.514