Question

In preparing to construct a one-sample t interval for a population mean, suppose we are not sure if the population distribution is Normal. In which of the following circumstances would we not be safe constructing the interval based on an SRS of size$14$from the population?

a. A stemplot of the data is roughly bell-shaped.

b. A histogram of the data shows slight skewness.

c. A boxplot shows that the values above the median are much more variable than the values below the median.

d. The sample standard deviation is large.

e. The sample standard deviation is small.

Short answer

The required correct option is$\left(c\right)$

Step-by-step solution

Given information

Sample size $\left(n\right)=14$

Confidence interval using $t$-distribution is to be constructed.

Explanation

When the sample size is less than $30$and the sample standard deviation is known, the confidence interval using the t distribution is computed. It is also used when data is normally distributed. Because it would show some variability in the data set, a box plot depicting values below and above the median would be inappropriate for constructing the confidence interval.

Therefore, under the circumstances of the box plot, it could be argued that constructing the confidence interval on a sample size of $14$is risky.

Hence, the correct option is$\left(c\right)$