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 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.)


(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 = 64

Point estimate = sample proportion = = x / n = 64 / 169=0.379

1 - = 1 - 0.379=0.621

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.96}

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

= 1.96 (((0.379*0.621) /169 )

= 0.0731

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.379 - 0.0731 < p <  0.379 + 0.0731

0.306< p < 0.452

The 95% confidence interval for the population proportion p is :(0.306 , 0.452)