Confidence intervals for means. [126.4, 132.2] is a 95% confidence interval for the mean mu of a normally distributed random variable with known variance. Find a 98% confidence interval for mu, based on the same sample.

Quinlan7g 2022-09-25 Answered
Confidence intervals for means
[126.4, 132.2] is a 95% confidence interval for the mean μ of a normally distributed random variable with known variance. Find a 98% confidence interval for μ, based on the same sample.
I got gamma = 0.98   g a m m a / 2 = 0.49   s o   Z = 2.33 but then I am lost on what to do next.
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Answers (1)

Cremolinoer
Answered 2022-09-26 Author has 11 answers
Step 1
The half-width of the 95% CI you're given is 2.9. The half-width of a 95% confidence interval for known variance σ 2 is
σ n ( 1.96 )
so this means σ n = 2.9 1.96 = 1.48.
Step 2
As your calculation shows, the half-width of a 98% CI is
σ n ( 2.33 )
so the half-width of your 98% CI must be
1.48 × 2.33 = 3.45.
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I have read two books that explicitly state that the ( 1 α )% confidence interval should be interpreted as:
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