Part III: Confidence Intervals for μ (σ known) Suppose IQ scores for adults follow a Normal...

Part III: Confidence Intervals for μ (σ known)

Suppose IQ scores for adults follow a Normal distribution with a standard deviation of 15. A random sample of 49 adults yields an average score of 100.

a) Construct 90%, 95%, and 99% confidence intervals for μ.

b) What is happening to the width of the confidence intervals as the confidence levels increase?

Explain why this makes sense both practically and mathematically (based upon the formula).

c) Using the known standard deviation of 15 and confidence level of 95%, construct 3 different

confidence intervals based upon sample sizes 49, 100, and 225, respectively.

d) What is happening to the width of the confidence intervals as the sample sizes increase?

Explain why this makes sense both practically and mathematically (based upon the formula).

Expert Solution

orchestra answered 1 year ago

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