Q242 · Practice questionTechnology-freeSimple familiar1 mark
QUESTION 242
A researcher reports an observed 95% confidence interval (8,12) for a fixed population mean. Which interpretation is valid?
(A)
The procedure captures the fixed mean in about 95 percent of repeated random samples.
(B)
Exactly 95 percent of individual observations lie between 8 and 12.
(C)
Exactly 95 percent of future sample means lie between 8 and 12.
(D)
The fixed mean now has probability 0.95 of lying between 8 and 12.
WORKED SOLUTION
1 markAnswer A
ANSWER
A. The procedure captures the fixed mean in about 95 percent of repeated random samples.
Worked solution
The parameter is fixed while random intervals vary between samples. Under its assumptions, the procedure has nominal 95 percent repeated-sampling coverage. D instead assigns a posterior probability to the fixed parameter, B concerns individuals, and C concerns future sample means.
Equivalent mathematically justified methods accepted.
Exact answers unless a decimal accuracy is specified.
Select A.
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