Question

I'm currently solving this, but I do not understand. If you can please show your work and formula. Thank you.

A random sample of 72 math majors generated the confidence interval (0.438, 0.642) to estimate the proportion of math majors that are female. What size sample would be necessary to estimate the true proportion within 2​% using 98​% ​reliability?

A. 3372

B. 3394

C. 3529

D. 3258

Answer 1

Solution :

Point estimate = = (Lower confidence interval + Upper confidence interval ) / 2

Point estimate = = (0.438 + 0.642) / 2

Point estimate = = 0.54

1 - = 1 - 0.54 = 0.46

margin of error = E = 0.02

At 98% confidence level

= 1 - 98%  

= 1 - 0.98 =0.02

/2 = 0.01

Z/2 = Z0.01 = 2.33

sample size = n = (Z / 2 / E )2 * * (1 - )

= (2.33 / 0.02)2 * 0.54 * 0.46

= 3371.34

sample size = n = 3372

correct option is = A