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 169 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

Solution : -

Given that,

n = 169

x = 66

Point estimate = sample proportion = = x / n = 66 / 169 = 0.3905

1 - = 1 - 0.391 = 0.6095

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.960

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 (((0.3905* 0.6095 ) / 169 )

= 0.074

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.3905 - 0.074 < p < 0.3905 + 0.074

0.3165 < p < 0.4645

( 0.317 , 0.465 )

A 95% confidence interval for population proportion p is ,

Lower limit = 0.317

Upper limit = 0.465