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 171 potsherds indicated that 66were 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

Given: Let the sample proportion of three-circle, red-on-white pattern potsherds be Let the event of success X be to obtain potsherds of three-circle, red-on-white pattern.

(a) From a sample of 171 potsherds (n = 171), x = 66 Hence,  

(b) 95% confidence interval for the population proportion p is computed using the formula:

where, z is obtained from the normal tables for 1 - = 1 - 0.05/2 = 0.975 area:

Z = 1.96

Substituting the values,

Hence, Lower limit = 0.313 Upper limit = 0.459