Problem-Solving and Data AnalysisVery hardComparing margins of error for two sample sizes
Problem-Solving and Data Analysis practice question
Two random samples are drawn from the same population to estimate its mean. Sample A has 100 people and sample B has 900 people. Which of the following best compares their margins of error?
- A. Sample B's margin of error is about one third of sample A's.Correct
- B. Sample B's margin of error is about one ninth of sample A's.
- C. The two margins of error are about the same.
- D. Sample B's margin of error is about three times sample A's.
Answer: A. Sample B's margin of error is about one third of sample A's.
The margin of error shrinks with the square root of the sample size, and the square root of 9 is 3.
Why the other answers are wrong
- B. Sample B's margin of error is about one ninth of sample A's.
- One ninth would apply if the margin shrank in direct proportion to the sample size.
- C. The two margins of error are about the same.
- A larger sample gives a smaller margin.
- D. Sample B's margin of error is about three times sample A's.
- Larger samples give smaller, not larger, margins.
More Problem-Solving and Data Analysis questions
- Very hard
An item priced at $200 is first marked down by 20%, and then an additional 10% is taken off the reduced price.… - Very hard
A data set of 6 test scores has a mean of 78. After a 7th score is added, the mean rises to 80. What was the 7… - Very hard
If one of the chips that failed inspection is selected at random, what is the probability that it was produced… - Very hard
The regular price of a bicycle at a shop was increased by 25%. Later, during a sale, this increased price was … - Very hard
What is the result when the mean number of pets is subtracted from the median number of pets? - Very hard
What is the value of x?
Not affiliated with the College Board. SAT is a trademark of the College Board.