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 64 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.)

= 0.3699

(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,

n = 173 ....... Sample size

x = 64 .......no. of successes in the sample

a)

Let denotes the sample proportion.

     = x/n   = 64 / 173 = 0.3699

Our aim is to construct 95% confidence interval.

c = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.025 and 1- /2 = 0.975

Search the probability 0.975 in the Z table and see corresponding z value

= 1.96

Now , the margin of error is given by

E = *  

= 1.96 * [0.3699 *(1 - 0.3699)/173]

= 0.07194157231

Now the confidence interval is given by

( - E)   ( + E)

(0.3699 - 0.07194157231)   (0.3699 + 0.07194157231)

0.298    0.442

Lower Limit = 0.298   

Upper Limit = 0.442