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 181 potsherds indicated that 70 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

Answer:

a)

Given,

To determine the point estimate

n = 181

x = 70

we know,

Point estimate = = x / n

substitute the values

= 70 / 181

Point estimate = 0.3867

b)

Now to determine the upper limit & lower limit

let us consider,

1 - = 1 - 0.3867

1 - = 0.6133

Here we know that, at the 95% confidence level the z value is , Z_/2 = Z_0.025 = 1.96

Margin of error = E

= Z _{/ 2} * (( * (1 - )) / n)

substitute the known values in above formula

= 1.96* (((0.3867 * 0.6133) / 181)

E = 0.0709

Now interval = +/- E

substitute the values

= (0.3867 +/- 0.0709)

= (0.3867 - 0.0709 , 0.3867 + 0.0709)

= (0.3158 , 0.4576)

Upper limit = 0.4576

Lower limit = 0.3158