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Chapter 10: Sampling Distributions and the Central Limit Theorem
Example 10-5:
Two large universities in a given state compete annually
and compare the proportion of graduates who pass the Certified Public
Accountant (CPA) examination on the first try.
Table 10-10
shows the
summary results for this year’s results for the two schools . It includes the
sample sizes (the number of students who took the exam for the first time)
and the number of successes (the number of students who passed the exam
on the first try).
Table 10-10:
InformationRelated to
Example 10-5
Based on past history, it is known that 75% of students who are from
University 1 are successfulwhile only 50% are successful from University
2. What is the probability that the difference in the proportion of success
from University 1 and University 2 is at least 10 percent?
Solution
: First we need to check whether the assumptions for the
normality approximation hold. Based on the information given
= 100,
= 45,
= 0.75,
= 0.50,
̂
1
= 70/100 = 0.7, and
̂
2
= 23/45 = 0.5111.
So,
= 100
0.75 = 75 > 5,
= 100
0.25 = 25 > 5,
=
45
0.5 = 22.5 > 5, and
= 45
0.5 = 22.5 > 5. Thus the