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M3-050-A08-V02
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S-IC.4
Warmup
M3-050-A08-V02
Use sample data to estimate population means/proportions and develop margins of error using simulation.
Apply an explicitly informal interval-overlap rule
Problem
The displayed estimates are \(A~=~51\%~\pm~4~\text{points}\) and \(B~=~48\%~\pm~4~\text{points}\). Compute \(\text{both}~\text{intervals}\), find their gap or overlap, and apply the stated informal rule without claiming a formal significance test.
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A
A is [47%, 55%] and B is [44%, 52%]. They overlap from 47% to 52%, which establishes a formal p-value and statistically significant difference.
B
A is [47%, 55%] and B is [44%, 52%]. They overlap from 47% to 52%, so the informal rule suggests a difference; this is not a formal significance test.
C
Ignore the margins and use A = [51%, 51%] and B = [48%, 48%]. Their 3-point gap suggests a difference under the informal rule, but this is not a formal significance test.
D
A is [47%, 55%] and B is [44%, 52%]. They overlap from 47% to 52%, so the informal rule gives no clear difference; this is not a formal significance test.
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Curriculum context
Standard S-IC.4
Category Statistics and Probability
Domain Making Inferences and Justifying Conclusions
Objective Use sample data to estimate population means/proportions and develop margins of error using simulation.
Problem type Apply an explicitly informal interval-overlap rule