Problem-Solving and Data AnalysisHardEffect of sample size on a margin of error
Problem-Solving and Data Analysis practice question
Two random polls estimate support for the same candidate. Poll A surveys 400 voters and Poll B surveys 1,600 voters. Poll B's margin of error is smaller than Poll A's by approximately what factor?
Answer: 2
The margin of error shrinks with the square root of the sample size, and √(1,600/400) = √4 = 2.
Common wrong answers
- If you answered 4
- 4 is the ratio of the sample sizes, not of the margins.
- If you answered 1200
- 1200 is the difference in sample sizes.
- If you answered 1.5
- 1.5 comes from a guess rather than the square-root rule.
More Problem-Solving and Data Analysis questions
- Hard
The mean of five numbers is 12. If four of them are 8, 10, 14, and 16, what is the fifth number? - Hard
In a survey of 50 people, 30 like coffee, 20 like tea, and 8 like both. How many like neither? - Hard
A car travels at 60 mph for 2 hours, then 40 mph for 3 hours. What is its average speed for the whole trip? - Hard
Which statement correctly compares the standard deviations of the two sets? - Hard
Which statement best interprets the slope of the line of best fit? - Hard
How many milliliters of the 40% acid solution must the chemist add?
Not affiliated with the College Board. SAT is a trademark of the College Board.