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 62 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 = 62

Point estimate = sample proportion = = x / n = 62/181=0.3425

1 - = 1-0.3425=0.6575

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 (((0.3425*0.6575) / 181)

E = 0.069

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.3425-0.069 < p < 0.3425+ 0.069

0.2735< p < 0.4115

The 95% confidence interval for the population proportion p is : lower limit=0.274,upper limit=0.412