Question

You are thinking of conducting a one-sample t-test about a population mean M using a $0.05$ significance level. You suspect that the distribution of the population is not Normal and may be moderately skewed. Which of the following statements is correct?

(a) You should not carry out the test because the population does not have a Normal distribution.

(b) You can safely carry out the test if your sample size is large and there are no outliers.

(c) You can safely carry out the test if there are no outliers, regardless of the sample size.

(d) You can carry out the test only if the population standard deviation is known.

(e) The $t$ procedures are robust—you can u

Short answer

The correct statement is (B), You can safely carry out the test if your sample size is large and there are no outliers.

Step-by-step solution

Given Information

A one-sample $t$test about a population mean $M$using a $0.05$ significance level.

Explanation

To identify the correct statement:

(a) False, because if a distribution is moderately skewed, then you can still carry out the test if the sample size is large ($30$or more).

(b) True, because if the sample size is larger ($30$ or more) and there are no outliers, then you can still safely carry out the test.

(c) False, the sample size should be large ($30$ or more) since the distribution is moderately skewed.

(d) False, the one-sample $t$ test can only be used if the population standard deviation is unknown. You apply the onesample $z$ test if the population standard deviation is known.

(e) False, $t$-procedures are not robust, because they are heavily influenced by outliers.

Therefore, the correct answer is (B).