Answer to Question #175744 in Statistics and Probability for Ajay Singh

Question

1.      A university system enrolling hundreds of thousands of students is considering a change in the way students pay for their education. Currently, the students pay $400 per credit hour. The university system administrators are contemplating charging each student a set fee of $7,000 per quarter, regardless of how many credit hours each takes. To see if this proposal would be economically feasible, the administrators would like to know how many credit hours, on the average, each student takes per quarter. A random sample of 250 students yields a mean of 14.1 credit hours per quarter and a standard deviation of 2.3 credit hours per quarter. Suppose the administration wanted to estimate the mean to within 0.1 hours at 95% reliability and assumed that the sample standard deviation provided a good estimate for the population standard deviation. How large a total sample would they need to take? (2)

 

Answer 1

Solution:

We know that $n=(\dfrac{z\times s}{E})^2$ ...(i)

where

n = minimum sample size

z = standard normal critical value

s = sample standard deviation, which approximates the population standard deviation  (sigma)

E = margin of error

And, given: s = 2.3, E = 0.1

For 95% confidence interval, the critical value is z = 1.96

Putting these values in (i),

$n=(\dfrac{z\times s}{E})^2=(\dfrac{1.96\times 2.3}{0.1})^2\approx2032.2064$

$\Rightarrow n=2033$ [Rounding off to next whole number]

Hence, the minimum sample size is 2033.