Question

a sample of 100 students was taken at random. each studen in the sample was asked whether or nt they intended to go to graduate school. 25 of the student said "yes they intend to go to graduate school." wht is the 95% confidence interval that would estimate the poplation proportion of students that intend to go to gradua school.

Answer 1

95% confident that the true population proportion of students who intend to go to graduate school is between 0.156 and 0.344.

The sample proportion of students who intend to go to graduate school is 25/100 = 0.25.

To calculate the 95% confidence interval, we need to find the margin of error. The margin of error is equal to 1.96 times the standard deviation of the sample proportion. The standard deviation of the sample proportion can be calculated using the formula:

sqrt(p(1-p)/n)

where:

p is the sample proportion

n is the sample size

In this case, the standard deviation of the sample proportion is:

sqrt((0.25)(0.75)/100) = 0.048

Therefore, the margin of error

1.96 * 0.048 = 0.094

The 95% confidence interval is then:

p +/- margin of error

which is:

0.25 +/- 0.094

or:

(0.156, 0.344)

We are 95% confident that the true population proportion of students who intend to go to graduate school is between 0.156 and 0.344.