Final answer:
A t procedure might not be appropriate in situation A, where there are multiple large outliers, as they can violate the normality assumption critical for the t-distribution. Options B and D are typically not severe enough to invalidate the t procedure, and option C is unrelated to the distribution shape.
Step-by-step explanation:
The t procedure may not be appropriate when data exhibits strong violations of the assumptions underlying the t-distribution, which are that the data come from a normally distributed population and that the sample size is sufficiently large to approximate the normal distribution when the population distribution is unknown.
Among the provided circumstances, option A, where a boxplot of the data has multiple large outliers, represents a situation where the t procedure might not be safe to use. This is because large outliers can significantly affect the mean and violate the normality assumption that is critical for the t-distribution to provide reliable inference.
Option B, where the mean and median of the data are nearly equal, suggests symmetry in the distribution, indicating that the t procedure would be appropriate. Option C, a large sample standard deviation, does not necessarily disqualify the use of a t procedure, assuming the sampling distribution of the mean is approximately normal. Lastly, option D, very slight skew as shown in a boxplot, is often considered tolerable, and the t procedure may still be used if the sample size is not too small and the skewness is not severe.