Confidence Region Calculations II
For each situation below, construct and interpret the confidence region.
- α=0.01, HA: μ≠800, n=25, σ=60, x̄=824.
- α=0.05, HA: μ<80, n=30, σ=20, x̄=73.
- α=0.05, HA: μ≠1500, n=40, σ=800, x̄=1370.
Confidence Regions Concepts
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FALSE, because x̄ is a statistic and confidence regions are only constructed for parameters.
TRUE, because the population median is a parameter, which confidence regions are computed for.
TRUE, because σ is a parameter, which confidence regions are computed for.
CAN'T TELL, because we never (in real-life) know the value of the parameter. We are 95% confident that the parameter is in that interval, but it will not be in 5% of confidence intervals.
PARAMETER. We are confident that the parameters is in the interal..
B, because the margin-of-error gets smaller, and the CI gets narrower, as $n$ increases.
C, because the margin-of-error is smaller, and the confidence interval is narrower, for smaller values of σ.
95%, because the Z* is smaller, the margin-of-error is smaller, and the confidence interval is narrower, for lower confidence values.
Finding Z*
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±2.576 as computed with distrib(0.995,type="q").
-1.405 as computed with distrib(0.92,type="q",lower.tail=FALSE).
1.282 as computed with distrib(0.90,type="q").
±2.326 as computed with distrib(0.99,type="q").
-1.645 as computed with distrib(0.95,type="q",lower.tail=FALSE).
0.524 as computed with distrib(0.70,type="q").