Question

To estimate the proportion of a large college who are female, a random sample of 120 students is selected. There are 69 female students in the sample. Assume that the sampling distribution is approximately normal. Construct a 90% confidence interval for the proportion of all students at the college who are female.

Answer 1

To construct a 90% confidence interval for the proportion of all students at the college who are female, we can use the formula CI = p' ± Z * sqrt((p' * (1 - p')) / n), where p' is the sample proportion, Z is the Z-value for the desired confidence level, and n is the sample size.

Step-by-step explanation:

To construct a 90% confidence interval for the proportion of all students at the college who are female, we can use the formula:

CI = p' ± Z * sqrt((p' * (1 - p')) / n)

Where p' is the sample proportion, Z is the Z-value for the desired confidence level, and n is the sample size. In this case, p' = 69/120 = 0.575, Z = 1.645 (for a 90% confidence level), and n = 120.

Plugging in the values, we get:

CI = 0.575 ± 1.645 * sqrt((0.575 * (1 - 0.575)) / 120)

Calculating this gives us the confidence interval (0.506, 0.644). This means that we can estimate with 90% confidence that the true proportion of all students at the college who are female is between 0.506 and 0.644.