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 5160 permanent dwellings on an entire reservation showed that 1620 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 all confidence intervals would include the true proportion of traditional hogans. 1% of the confidence intervals created using this method 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. 99% 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 normal. No, the conditions are not 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. No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.

Answer 1

Answer)

A)

Point estimate = 1620/5160 = 0.31395348837 = 0.314

B)

N = 5160

P = 1620/5160

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 1620

N*(1-p) = 3540

Both the conditions are met so we can use standard normal z table to estimate the interval

Critical value z for 99% confidence level, from z table is 2.576

Margin of error (MOE) = Z*√P*(1-P)/√N

Z = 2.576

N = 5160

P = 0.314

After substitution

MOE = 0.01664362376

Confidence interval is given by

P-MOE < P < P+MOE

0.29735637623 < P < 0.33064362376

Lower limit = 0.297

Upper limit = 0.331

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

C)

Yes satisfied we have already checked the conditions in part B

This is important as it allows us to assume that p is approximately normal.