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 165 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 = 165

x = 78

Point estimate = sample proportion = = x / n = 78/165=0.4727

1 - = 1-0.473=0.5273

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

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

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

= 1.96 (((0.4727*0.5273) /165 )

E = 0.076

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.4727-0.076< p <0.4727+ 0.076

0.397< p < 0.549

The 95% confidence interval for the population proportion p is : lower limit =0.397,upper limit= 0.549