Suppose you mistakenly used the standard normal distribution to form a 95% confi

Question

Suppose you mistakenly used the standard normal distribution to form a 95% confidence interval for the population mean (using the sample mean as the pivotal statistic) when you should have used a Student t distribution.

a. How much bigger should the confidence interval be, in the worst case?

b. How large would the sample have to be in order for the erroneous confidence interval to have a width within 5% of what it should have had?

c. How do the answers to a) and b) change if we increase the confidence level? Explain why this is REALLY important.

Explanation / Answer

a. The confidence interval is should be 0.025 bigger than the previous interval.

b.

c. Increasing the confidence level of a confidence interval will only result in larger intervals.

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