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 161 potsherds indicated that 66 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

ANSWER:

Given that,

Sample size (n) = 161

x = No. of successes = No. of potsherds of three-circle, red-on-white pattern =66

a)

= x / n = 66 / 161 = 0.4099

1 - = 1 - 0.4099 = 0.5901

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 * (((0.4099 * 0.5901) / 161)

= 0..0759

A 95% confidence interval for population proportion p is ,

- E < P < + E

0.4099 - 0.0759 < p < 0.4099 + 0.0759

0.334  < p < 0.486

Lower limit = 0.334

Upper limit = 0.486