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 known. When constructing the confidence interval, the researcher should use the normal distribution; however, she incorrectly uses the t distribution. How does this incorrectly calculated confidence relate to the correct confidence interval?
A)The calculated confidence interval is shifted to the right of the correct confidence interval.
B)The calculated confidence interval is narrower than the correct confidence interval.
C)The calculated confidence interval is wider than the correct confidence interval.
D)The calculated confidence interval is shifted to the left of the correct confidence interval.

Question

Quizplus · Accepted Answer

When the sample size is small (n < 30) and the population standard deviation is known, the correct approach is to use the normal distribution for constructing confidence intervals. However, if one incorrectly uses the t-distribution instead, the resulting confidence interval will be wider than the correct interval. This is because the t-distribution accounts for the additional uncertainty introduced by estimating the population standard deviation from the sample, leading to wider intervals to maintain the same level of confidence.

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