Question

A statistician constructed a confidence interval for the mean μ of a population and the result was the interval (25,30). Which of the following statements is/are true?

1. There is a 0.9 probability μ is between 25 and 30.
2. If 100 random samples of the same size are picked and a 90% confidence interval is calculated from each one, then μ will be in 90 of those 100 confidence intervals.
3. If 90% confidence intervals are calculated from all possible samples of the same size, μ will be in 90% of those confidence intervals.

Group of answer choices

Statements 1 and 2, but not 3, are true.

Statements 1 and 3, but not 2, are true.

Statements 2 and 3, but not 1, are true.

All three statements are true.

None of the choices above capture the exact set of true statements.

Answer 1

Statements 2 and 3, but not 1, are true.

true statements are

If 100 random samples of the same size are picked and a 90% confidence interval is calculated from each one, then μ will be in 90 of those 100 confidence intervals.

If 90% confidence intervals are calculated from all possible samples of the same size, μ will be in 90% of those confidence intervals

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