Question

# 2). A survey conducted by Sallie Mae of 700 college students found that 323 students paid...

2). A survey conducted by Sallie Mae of 700 college students found that 323 students paid for their education by student loans.
a) Find the best point estimate for the true proportion: ______________
b) Find the 95% confidence of the true proportion of students who paid for their education by student loans.
__________________________
c) The Department of Education in State of Louisiana believes that the proportion of students that pay for their education using student loans is around 75%. Based on the sample above do you agree or disagree with that state

A survey conducted by Sallie Mae of 700 college students found that 323 students paid for their education by student loans.

Therefore

a) Thus Best points estimate for the true population is,

b) The 95% confidence interval is given by,

Here for 95% C.I. i.e. for alpha =0.05, from Z table,

Thus

The 95% confidence of the true proportion of students who paid for their education by student loans is (0.4231, 0.4969)

c) I have disagree with The Department of Education in State of Louisiana statement that the proportion of students that pay for their education using student loans is around 75%

because 75% i.e. 0.75 is outside of our 95% Confidence interval.

As Proportion is lies between 0.42 and 0.50 in 95% confidence interval.

So we are disagree with the state.