ACS 5-year estimates show 2,400 households below poverty in Tract 12 (MOE ±300) and 2,100 in Tract 14 (MOE ±350), both at 90 percent confidence. A council member says Tract 12 clearly has more households in poverty. Which conclusion is BEST supported?
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Answer: B
- Difference between estimates = 2,400 − 2,100 = 300.
- MOE of the difference = √(300² + 350²) = √(90,000 + 122,500) = √212,500 ≈ 461.
- Since 300 < 461, the difference is not statistically significant at the 90 percent level.
Tract 12 has significantly more, since its estimate is 300 higher: This ignores sampling error. A difference must exceed its own MOE to be significant.
The difference is not significant; 300 is below its MOE of about 461: Correct. The MOE of a difference is the square root of the sum of the squared MOEs: √(300² + 350²) = √212,500 ≈ 461. The 300-household difference is smaller than 461, so the tracts are not statistically different at 90 percent confidence.
The difference is significant because the MOE of the difference is 50: This subtracts the MOEs (350 − 300). MOEs combine as the square root of the sum of squares.
Significance cannot be judged without a decennial census count: The decennial census does not collect poverty data. ACS MOEs are designed for this test.
Before comparing ACS estimates, test the difference: MOE(diff) = √(MOE₁² + MOE₂²); significant only if |difference| > MOE(diff).