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 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 *p̂* is approximately normal.

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

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

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

Answer #1

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.

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 368 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...

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

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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 576 potsherds was found, of which 366 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...

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 576 potsherds was found, of which 353 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...

For this problem, carry at least four digits after the decimal
in your calculations. Answers may vary slightly due to
rounding.
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archaeological excavations at a certain monument. At one excavation
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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...

For this problem, carry at least four digits after the decimal
in your calculations. Answers may vary slightly due to
rounding.
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archaeological excavations at a certain monument. At one excavation
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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...

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 576 potsherds was found, of which 363 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...

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 570 potsherds was found, of which 353 were
identified as Santa Fe black-on-white.
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