Question

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

Santa Fe black-on-white is a type of pottery commonly found at archaeological excavations at a certain monument. At one excavation site a sample of 578 potsherds was found, of which 360 were identified as Santa Fe black-on-white.

(a) Let p represent the proportion of Santa Fe black-on-white potsherds at the excavation site. Find a point estimate for p. (Round your answer to four decimal places.)


(b) Find a 95% confidence interval for p. (Round your answers to three decimal places.)

Lower Limit =

Upper Limit =

Answer 1

Solution :

Given that,

n = 578

x = 360

a) Point estimate = sample proportion = = x / n = 360 / 578 = 0.6228

1 - = 1 -0.623 = 0.3772

b) At 95% confidence level

= 1-0.95% =1-0.95 =0.05

/2 =0.05/ 2= 0.025

Z/2 = Z0.025 = 1.960

Z/2 = 1.960

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

= 1.960 * ((0.6228*(0.3772) /578 )

= 0.040

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.623 -0.040 < p < 0.623+0.040

0.583 < p < 0.663

( 0.583 ,0.663 )

Lower Limit =0.583

Upper Limit =0.663