Question

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

Answer #1

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.

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