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 167 potsherds indicated that 76 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 = 167

x = 76

a) Point estimate = sample proportion = = x / n = 76 /167 = 0.4551

1 - = 1 -0.4551 = 0.5449

b) At 95% confidence level

= 1-0.95% =1-0.95 =0.05

/2 =0.05/ 2= 0.025

Z/2 = Z0.025 = 1.960

Z/2 = 1.960

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

= 1.960 * ((0.4551*(0.5449) /167 )

= 0.076

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.4551 - 0.076 < p < 0.4551 +0.076

0.379 < p < 0.531  

(0.379 , 0.531 )

Lower limit = 0.379

Upper limit = 0.531