Solve the problem.
-A researcher wishes to construct a 95% confidence interval for a population mean. She selects a simple random sample of size n = 20 from the population. The population is normally distributed and is unknown. When constructing the confidence interval, the researcher should use the t distribution; however, she incorrectly uses the normal distribution. Will the true confidence level of the resulting confidence interval be greater than 95%, smaller than 95%, or exactly 95%?
A)Greater than 95%
B)Exactly 95%
C)Smaller than 95%

Question

Quizplus · Accepted Answer

The t distribution is wider and has heavier tails than the normal distribution, especially for small sample sizes (n < 30). Using the normal distribution instead of the t distribution results in a narrower confidence interval, which underestimates the variability in the sample. Therefore, the true confidence level of the resulting interval will be smaller than 95%.

Solve the Problem. -A Researcher Wishes to Construct a 95% Confidence Interval for Confidence