Question

A report says that 82% of British Columbians over the age of 25 are high school graduates. A survey of randomly selected residents of a certain city included 1290 who were over the age of 25, and 1012 of them were high school graduates.

Part a
Which of the following gives the approximated model for the sample proportion of high school graduates in a sample of 1290 students?
Answer:  Select one N(0.78,0.011) N(0.82,0.011) N(78,1.11) N(82,1.11) N(1012, 13.80)

Part b
How many standard deviation away is the sample proportion of high school graduates (1012/1290) is away from the mean? You will need to use the correct approximated model to answer the question.
Answer:  Select one Less than -2 Between -2 and -1 Between -1 and 1 Between 1 and 2 More than 2

Part c
Is the city's result of 1012 unusually high, low, or neither? You will need to use the correct approximated model to answer the question.
Answer:  Select one High Low Neither

Answer 1

Solution:
Given in the question
Population proportion = 0.82
Sample size = 1290
Solution(a)
approximated model for the sample proportion is
Sample proportion = 0.82
Sample standard error of proportion = sqrt(p*(1-p)/n) = sqrt(0.82*(1-0.82)/1290) = sqrt(0.0001) = 0.0107 or 0.011
So approximate model for sample proportion is N(0.82,0.011) , So its answer is B
Solution(b)
sample proportion = 1012/1290 = 0.78
test stat = (sample proportion - Population proportion)/sqrt(population proportion*(1-population proportion)/n) = (0.78-0.82)/sqrt(0.82*0.18/1290) = -3.74
its answer is A. i.e. Less than -2
Solution(c)
as we can see that test stat value is less than 2 so city's result of 1012 is unusually low.
So its answer is B. i.e. Low