Question: With everything else remaining the same... INCREASING the sample size n causes the width of a Confidence Interval to INCREASE, DECREASE, or STAY THE SAME?

With everything else remaining the same... INCREASING the sample size n causes the width of a Confidence Interval to INCREASE, DECREASE, or STAY THE SAME? Explain your answer.

With everything else remaining the same... INCREASING the population standard deviation causes the width of a Confidence Interval to INCREASE, DECREASE, or STAY THE SAME? Explain your answer.

With everything else remaining the same INCREASING your level of confidence (from 90% to 95%, for example) causes the width of a Confidence Interval to INCREASE, DECREASE, or STAY THE SAME? Explain your answer.

The higher the confidence level, the more confident we can be that our confidence interval contains the population mean. Why is it that we don't always want to compute confidence intervals at very high confidence levels, say at 99% or 99.9%?

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