Question

If n=200 and p' (p-prime) = 0.78, construct a 90% confidence interval. Give your answers

Answer 1

To construct a 90% confidence interval for n = 200 and p' = 0.78, calculate the estimated proportion of failures (q'), the standard error (SE), the margin of error (ME), and then the confidence interval.

Step-by-step explanation:

To calculate the 90% confidence interval, we first need to find the estimated proportion of successes (p') and the estimated proportion of failures (q').

1. Given n = 200 and p' = 0.78
2. q' = 1 - p' = 1 - 0.78 = 0.22
3. Calculate the standard error (SE): SE = sqrt((p' * q') / n) = sqrt((0.78 * 0.22) / 200) ≈ 0.031
4. Calculate the margin of error (ME): ME = z * SE, where z is the z-score for the desired confidence level. For a 90% confidence level, z ≈ 1.645
5. ME ≈ 1.645 * 0.031 ≈ 0.051
6. The 90% confidence interval is given by (p' - ME, p' + ME) = (0.78 - 0.051, 0.78 + 0.051) = (0.729, 0.831)