Question

#1: Total students 237, total males 41, need to estimate the proportion of students that are male using 90% confidece level.
Also #2: estimate the proportion of students that commute less than 5 miles to work within 2% , what sample size would you need. Total students 237. total # that commute less than 5 miles is 20.
I need ASAP. I've tried and can't get it.

Answer 1

Example of a proportional confidence interval formula:

CI90 = p + or - (1.645)[√(pq/n)]
...where p = x/n, q = 1 - p, and n = sample size.
Note: + or - 1.645 represents 90% confidence interval.

For p in your problem: 41/237
For q: 1 - p = q
n = 237

I let you take it from here to calculate the interval. (Note: convert all fractions to decimals.)

Formula to find sample size:
n = [(z-value)^2 * p * q]/E^2
... where n = sample size, z-value is found using a z-table for confidence level, p = 20/237, q = 1 - p, ^2 means squared, * means to multiply, and E = .02 (2%).

Plug values into the formula and calculate n. (Remember to convert all fractions to decimals.)

I hope this will help get you started.