Question

A 99% confidence interval for a proportion p is (54%, 58%). Which of the following statements is true:

1. There is a 99% probability that p is between 54% and 58%.

2. If we took indefinitely many independent SRS’s of the same size and from each computed a 99% confidence interval for p, then approximately 99% of these intervals would contain p .

3. If we took indefinitely many independent SRS ’ s of the same size and from each computed a 99% confidence interval for p , then approximately 99% of these intervals would equal (54%, 58%).

4. None of these    

A 99% confidence interval for a proportion p is (54%, 58%). Which of the following statements is true:

  1.There is a 99% probability that p is between 54% and 58%.

2. In repeated independent SRS’s, approximately 99% of all sample proportions would fall between 54% and 58%.

3. If we took indefinitely many independent SRS’s of the same size and from each computed a 99% confidence interval for p , then approximately 99% of these intervals would equal (54%, 58%).

4. None of these

Please show all steps, explain and how to calculate

Answer 1

(1)

Correct option:

2.   If we took indefinitely many independent SRS's of same size and from each computed a 99% confidence interval for p, then approximately 99% of these intervals would contain p.

Explanation:

99% confidence interval : p is between 54% and 58% is a range of values that is likly to contain unknown population proportion. If we draw a random sample many times, 99% of the confidence intervals will contain the population proportion.

(2)

Correct option:

4. None of these

Explanation:

Explanation:

99% confidence interval : p is between 54% and 58% is a range of values that is likley to contain unknown population proportion. If we draw a random sample many times, 99% of the confidence intervals will contain the population proportion. We note none of the given options satisfy the above fact and none of them is applicable.