Question

# For this problem, carry at least four digits after the decimal in your calculations. Answers may...

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 586 potsherds was found, of which 358 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

Give a brief statement of the meaning of the confidence interval.

95% of the confidence intervals created using this method would include the true proportion of potsherds.

95% of all confidence intervals would include the true proportion of potsherds.

5% of the confidence intervals created using this method would include the true proportion of potsherds.

5% of all confidence intervals would include the true proportion of potsherds.

(c) Do you think that np > 5 and nq > 5 are satisfied for this problem? Explain why this would be an important consideration.

No, the conditions are not satisfied. This is important because it allows us to say that is approximately normal.

No, the conditions are not satisfied. This is important because it allows us to say that is approximately binomial.

Yes, the conditions are satisfied. This is important because it allows us to say that is approximately normal.

Yes, the conditions are satisfied. This is important because it allows us to say that is approximately binomial.

a)
sample proportion, pcap = 0.6109

b)
sample size, n = 586
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.6109 * (1 - 0.6109)/586) = 0.0201

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.6109 - 1.96 * 0.0201 , 0.6109 + 1.96 * 0.0201)
CI = (0.572 , 0.650)

lower limit = 0.572
upper limit = 0.650

95% of the confidence intervals created using this method would include the true proportion of potsherds.

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.