Question

1. To study what proportion of students will take statistics at UCW, undergrad students were repeatedly sampled with samples of size 36. The sampling distribution shows that 80% of them must take this course to complete a degree. What is the probability that more than 85% of the UCW students take statistics? What is the standard error of the population proportion?

Answer 1

Result:

To study what proportion of students will take statistics at UCW, undergrad students were repeatedly sampled with samples of size 36. The sampling distribution shows that 80% of them must take this course to complete a degree. What is the probability that more than 85% of the UCW students take statistics? What is the standard error of the population proportion? (4 marks)

Normal approximation to binomial distribution used.

n=36, p=0.80

standard error = sqrt( p*(1-p)/n) = sqrt(0.8*0.2/36) = 0.0667

z value for the proportion 0.85, z = (0.85-0.80)/0.0667 = 0.75 ( 2 decimals)

P( p>0.85) = P( z > 0.75)

=0.2266

The required probability = 0.2266

Excel function used to get probability: =1-NORM.S.DIST(0.75,TRUE)