In a random sample of 684 observations,

p-bar = 0.3. What lower bound of a 90% confidence interval for p?

Round to four decimal places for all your calculations, including the FINAL answer.

1 answer

The formula for a confidence interval for a proportion is:

p ± z*√(p*(1-p)/n)

where p is the sample proportion, z is the z-score corresponding to the desired confidence level, and n is the sample size.

For a 90% confidence interval, the z-score is 1.645.

Plugging in the values, we get:

0.3 ± 1.645*√(0.3*(1-0.3)/684)

Simplifying:

0.3 ± 0.0493

The lower bound of the confidence interval is:

0.3 - 0.0493 = 0.2507

Rounded to four decimal places:

0.2507