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 19 potsherds indicated that were of the three-circle, red-on-white pattern 

(a) Find a point estimate p for the proportion of all ceramic potsherds at this site that are of the three-cinder, 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 : n=179 , X=80

a) The estimate of the sample size is ,

80 p= = 0.4469 n 179

Now , the critical value is , $Z_{\alpha/2}=Z_{0.05/2}=1.96$ ; FRom Z-table

b) Therefore , the 95% confidence interval is ,

$\hat{p}\pm Z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$

$0.4469\pm 1.96*\sqrt{\frac{0.4469(1-0.4469)}{179}}$

$0.4469\pm 0.0728$

Lower limit=0.374

Upper limit=0.520