Math question about Statistic

Question

1. Students need to score 30 or above in the final exam to pass a module at University A. Assume final exam score is normally distributed.

 

(a) The teacher of STAT101, a module at University A, would like to estimate the proportion of students who pass the module to within 10% with 90% confidence. How large a sample should he take if he believes that the sample proportion is between 0.9 and 0.95 (inclusive)?

Answer 1

Thank you for your question Andy!

In order to answer this one you want to use the population proportion sample size formula

n = (Z*^2 * p * (1 – p)) / E^2

where n is the sample size

Z* is the critical value for that confidence level

p is the estimated proportion

and E is the margin of error

so plugging in the values we know on this one that would be

n = 1.645^2 * 0.95(1-0.95) / (0.10)^2

n = 54.7

since it’s a sample size you can round that up to the nearest whole number of 55 :)