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 5400 permanent dwellings on an entire reservation showed that 1648 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.

99% of all confidence intervals would include the true proportion of traditional hogans.

1% 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 the confidence intervals created using this method 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.

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 normal.

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

Answer 1

A random sample of 5400 permanent dwellings on an entire reservation showed that 1648 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.)

Let X be the variable of the no. of permanent dwelligns on an entire reservation.

This is an example of binomial distribution.

where is the an estimate for population 'p' .

= 0.3052

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

99% confidence interval for binomial proportion is

= 0.01

= 2.5758 .......using normal percentage table

lower limit	0.2890
upper limit	0.3212

Give a brief interpretation of the confidence interval.

Using 99% confidence interval, we can be 99% confident that the true proportion would lie within the calculated range.This is best explained by  

99% of all confidence intervals would include the true proportion of traditional hogans.

1% 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 the confidence intervals created using this method 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.

np = 1648 > 5

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 normal.     

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

This is because we can use asymptotic distribution for binomial by approximating it to normal distribution. Where

normal mean = np and normal variation = np(1-p)

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