Question

A confidence interval was used to estimate the proportion of math majors that are female. A random sample of 72 math majors generated the following confidence interval: (0.438, 0.642). Using the information above, what size sample would be necessary if we wanted to estimate the true proportion to within 5% using 95% reliability?

a. 396

b. 400

c. 385

d. 382

Answer 1

Solution:

Given: A random sample of 72 math majors generated the following confidence interval: (0.438, 0.642)

thus sample proportion is:

We have to find sample size n:

E = Margin of Error = 5% = 0.05

c = confidence level = 95%

Formula:

We need to find z_c value for c=95% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750

Look in z table for Area = 0.9750 or its closest area and find z value.

Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96

That is : Z_c = 1.96

Thus

Thus correct answer is:

d. 382