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 161 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

*ANSWER:*

*Given that,*

Sample size (n) = 161

x = No. of successes = No. of potsherds of three-circle, red-on-white pattern =66

*a)*

= x / n = 66 / 161 = 0.4099

1 - = 1 - 0.4099 = 0.5901

*b)*

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_{/2}
= Z_{0.025} = 1.96

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

= 1.96 * (((0.4099 * 0.5901) / 161)

= 0..0759

A 95% confidence interval for population proportion p is ,

- E < P < + E

0.4099 - 0.0759 < p < 0.4099 + 0.0759

0.334 < p < 0.486

Lower limit = **0.334**

Upper limit = **0.486**

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Question #1
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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...

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