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Which of the following statements about confidence intervals are true? I. A 95% confidence interval will...

Which of the following statements about confidence intervals are true?

I. A 95% confidence interval will contain the true μ 95% of the time.

II. If P(|X̅ − μ| > 3) = 0.035. Then a value of μ that is 3 or less units away from X̅ will be included in the 99% confidence interval.

III. The point estimate X̅ will be included in a 99% confidence interval.

Math   Statistics-And-Probability   
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Answer #1

It is true that 95% confidence interval will contain the true mean 95% of the time.

P(|X̅ − μ| > 3) = 0.035

=> P(|X̅ − μ| < 3) = 1 - 0.035

=> P(|X̅ − μ| < 3) = 0.965

=> P(|X̅ − μ| < 3) < 0.99

Then a value of μ that is 3 or less units away from X̅ will be included in the 99% confidence interval.

The point estimate X̅ is the estimate of true mean and will always included in a confidence interval. Thus III is a correct statement.

Thus, all statements I , II and III are true.

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