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 163 potsherds indicated that 78 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

GIVEN:

Sample size of ceramic potsherds

Number of ceramic potsherds who were of the three-circle, red-on-white pattern

SOLUTION:

(a) POINT ESTIMATE FOR PROPORTION OF CERAMIC POTSHERDS THAT ARE OF THREE-CIRCLE, RED-ON-WHITE PATTERN:

The point estimate (sample proportion) of all ceramic potsherds at this site of three-circle, red-on-white pattern is,

  

The point estimate (sample proportion) of all ceramic potsherds at this site of three-circle, red-on-white pattern is .

(b) % CONFIDENCE INTERVAL FOR POPULATION PROPORTION:

The formula for % confidence interval for population proportion is given by,

where is the z critical value at 95% confidence level.

CRITICAL VALUE:

The z critical value at 95% confidence level is .

CALCULATION:

The % confidence interval for population proportion of all ceramic potsherds with this distinctive pattern found at the site is,

The % confidence interval for population proportion of all ceramic potsherds with this distinctive pattern found at the site is .

The lower limit is .

The upper limit is .