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 5020 permanent dwellings on an entire 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 answer to three decimal places.)

lower limit
upper limit

Give a brief interpretation of the confidence interval.

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

Answer 1

a)

Point estimate of p = = 1676 / 5020 = 0.334

b)

99% confidence interval for p is

- Z * sqrt ( ( 1 - ) / n) < p < + Z * sqrt ( ( 1 - ) / n)

0.334 - 2.576 * sqrt( 0.334 * 0.666 / 5020) < P < 0.334 + 2.576 * sqrt( 0.334 * 0.666 / 5020)

0.317 < p < 0.351

Lower limit = 0.317

Upper limit = 0.351

c)

Since np = 5020 * 0.334 = 1976 > 5 and n(1-p) = 5020 * 0.666 = 3044 > 5

The conditions are satisfied.

In order to carry out this proportion test, we need to assume normal distribution .

So these conditions are necessary to satisfy.