PS.ED.3
Construct simulated sampling distributions of sample proportions and use sampling distributions to identify which proportions are likely to be found in a sample of a given size.
Example Problems
A credit union claims that 35% of its roughly 70,000 cardholders use automatic payments. A financial blogger takes a simple random sample of 280 cardholders and asks about autopay.
Assuming the credit union's claim is correct, what is the probability that the sample result is within 4 percentage points of the 35% claim?
Round your answer to the nearest hundredth.
Assuming the credit union's claim is correct, what is the probability that the sample result is within 4 percentage points of the 35% claim?
Round your answer to the nearest hundredth.
A newsletter team claims that 47% of its more than 200,000 subscribers opened the most recent email. An auditor takes a simple random sample of 160 subscribers and checks whether they opened it.
Assuming the team's 47% claim is correct, what is the approximate probability that more than 50% of the sample opened the email?
Round your answer to the nearest hundredth.
Assuming the team's 47% claim is correct, what is the approximate probability that more than 50% of the sample opened the email?
Round your answer to the nearest hundredth.
A factory's defect rate for microchips has been 2.4%. After installing a new quality-control system, engineers want to test if the defect rate has changed. In a production run of 3,000 chips, 81 were defective (2.7%).
Let represent the proportion of defective microchips with the new system.
State the alternative hypothesis, , for this test.
Let represent the proportion of defective microchips with the new system.
State the alternative hypothesis, , for this test.
Khan Academy Resources
1-on-1 AI tutoring aligned to PS.ED.3. Instant help for students, real-time insights for teachers.
Used in classrooms by 100,000+ students at Baltimore County, Plano ISD, Deer Valley USD, KIPP, and districts nationwide.
Free for teachers, forever →