Confidence interval

Question

Giving a test to a group of students, the grades and gender are summarized below

A	B	C	Total
Male	12	16	20	48
Female	3	19	10	32
Total	15	35	30	80

Let π� represent the percentage of all male students who would receive a grade of C on this test. Use a 99% confidence interval to estimate p to three decimal places.

Enter your answer as a tri-linear inequality using decimals (not percents).

 < p < 

Answer 1

The standard assumption when constructing confidence intervals is that you can apply a normal distribtuion. Therefore your z-critical value is 2.576 (approximately).

The lower bound of your confidence interval is given by the formula: mean - z_critical * standard error

The upper bound of your confidence interval is given by the formula: mean + z_critical * standard error

What is different here is that you are working with proportions, which changes how we calculate the mean and standard error.

mean: 20/48 = 0.417 (approximately)

standard error: sqrt((20/48)(1-(20/48))/48) = 0.071 (approximately)

lower bound = 0.233 (approximately)

upper bound = 0.600 (approximately)

Therefore, 0.233 < p < 0.600