In developing a confidence interval estimate for the population mean, which of the following is true?
A) The larger the sample standard deviation, the wider will be the interval estimate, all other things being equal.
B) If the population standard deviation is unknown, the appropriate critical value should be obtained from the t-distribution.
C) The confidence interval developed from a smaller sample size will have a larger margin of error than one obtained using a larger sample size, all other things being equal.
D) All of the above are true.

Question

Quizplus · Accepted Answer

Each statement is true regarding the development of a confidence interval estimate for the population mean. A) A larger sample standard deviation results in a wider confidence interval because the variability in the data is greater. B) When the population standard deviation is unknown, the t-distribution is used to account for the added uncertainty of estimating the population standard deviation from the sample. C) A smaller sample size leads to a larger margin of error because there is less information about the population, making the estimate less precise.

In Developing a Confidence Interval Estimate for the Population Mean