1. A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability, how many students would need to be sampled?

a) n = 1,844

b) n = 1,784

c) n = 1,503

d) n = 1,435

If I'm not mistaken, we use the formula n=(Z^2(P(1-P)))/e^2

Z=2.58

P=118/200

e=0.03

With these numbers, I get the answer 1789.9 ---> 1790, but this is not an available answer. What am I doing wrong?

ALSO, due to a shortage of credits, I need to squeeze another question here.

2. A major department store chain is interested in estimating the average amount its

credit card customers spent on their first visit to the chains new store in the mall.

Fifteen credit card accounts were randomly sampled and analyzed with the following

results: sample mean = $50.50, and s^2=400 . Construct a 95% confidence interval for the averageamount its credit card customers spent on their first visit

to the chains new store in the mall.

A) 50.50 +- 9.09

B) 50.50 +- 10.12

C) 50.50 +- 11.00

D) 50.50 +- 11.08

If I'm not mistaken, we use (xbar +- t(s/sqrt n))

n=15 degree of freedom = 14

xbar = 50.50

s^2 = 400 so s=20????

We find the value of t, which I found to be 2.1148 and used to formulas to get a variation of $10.92, which is not an answer. What am I doing wrong here?