Question

High School Diplomas

Statistics Canada reported in 2011 that 90% of Canadians aged 20–24 have a high school diploma.

a. Suppose you took a random sample of 2000 Canadians between the ages of 20 and 24.

What proportion would you expect to have a high school diploma?

How many young Canadians is this?

What proportion would you expect not to have a high school diploma?

How many young Canadians is this?

Are both numbers at least equal to 10, as required by the Central Limit Theorem?

b. If you took a random sample of 2000 Canadians between the ages of 20 and 24, find the probability that 91% or more will have earned a high school diploma.

Answer 1

a) The proportion of having a high school diploma = 0.90

Number of young Canadians = 2000 * 0.90 = 1800

The proportion of do not have a high school diploma = 1 - 0.9 = 0.1

Number of young Canadians = 2000 * 0.1 = 200

Yes, both numbers are at least equal to 10.

b) = p = 0.9

= sqrt(p(1 - p)/n)

= sqrt(0.9(1 - 0.9)/2000)

= 0.0067

P( > 0.91)

= P(( - )/ > (0.91 - )/)

= P(Z > (0.91 - 0.9)/0.0067)

= P(Z > 1.49)

= 1 - P(Z < 1.49)

= 1 - 0.9319

= 0.0681