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 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 = 173

x = 80

a) Point Estimate ()

= x / n = 80/173 = 0.4624

1 - = 1 - 0.4624 = 0.5376

b)

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z _{/ 2} * [ * (1 - ) / n]

= 1.96 * [(0.4624 * 0.5376) / 173]

= 0.0742

A 95% confidence interval for population proportion p is ,

- E < P < + E

0.4624 - 0.0742 < p < 0.4624 + 0.0742

0.3882 < p < 0.5366

(0.388, 0.537)