Question

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

A random sample of 5200 permanent dwellings on an entire
reservation showed that 1578 were traditional hogans.

(a) Let *p* be the proportion of all permanent dwellings
on the entire reservation that are traditional hogans. Find a point
estimate for *p*. (Round your answer to four decimal
places.)

(b) Find a 99% confidence interval for *p*. (Round your
answer to three decimal places.)

lower limit | |

upper limit |

Give a brief interpretation of the confidence interval.

1% of the confidence intervals created using this method would include the true proportion of traditional hogans.99% of all confidence intervals would include the true proportion of traditional hogans. 99% of the confidence intervals created using this method would include the true proportion of traditional hogans.1% of all confidence intervals would include the true proportion of traditional hogans.

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

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

Answer #1

a) Sample proportion = 1578/5200 = **0.3035**

b) For 99% confidence interval, z = 2.576

Hence,

99% confidence interval will be:

(0.287, 0.320)

Lower limit = **0.287**

Upper limit = **0.320**

Brief interpretation: 99% of the confidence intervals created using this method would include the true proportion of traditional hogans.

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

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in your calculations. Answers may vary slightly due to
rounding.
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reservation showed that 1683 were traditional hogans.
(a) Let p be the proportion of all permanent dwellings
on the entire reservation that are traditional hogans. Find a point
estimate for p. (Round your answer to four decimal
places.)
(b) Find a 99% confidence interval for p. (Round your
answer...

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in your calculations. Answers may vary slightly due to
rounding.
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reservation showed that 1683 were traditional hogans.
(a) Let p be the proportion of all permanent dwellings
on the entire reservation that are traditional hogans. Find a point
estimate for p. (Round your answer to four decimal
places.)
(b) Find a 99% confidence interval for p. (Round your
answer...

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in your calculations. Answers may vary slightly due to
rounding.
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reservation showed that 1676 were traditional hogans.
(a) Let p be the proportion of all permanent dwellings
on the entire reservation that are traditional hogans. Find a point
estimate for p. (Round your answer to four decimal
places.)
(b) Find a 99% confidence interval for p. (Round your
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