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 $24$from the population?

(a) A stem plot of the data is roughly bell-shaped.

(b) A histogram of the data shows slight skewness.

(c) A stem plot of the data has a large outlier.

(d) The sample standard deviation is large.

(c) The $t$procedures are robust, so it is always safe.

Short answer

(c) A stemplot of the data has a larger outlier.

Step-by-step solution

Step-1 Given Information

Given in the question that ,

sample size$\left(n\right)=24$

sampling is sampling random. we have to find the correct option.

Step-2 Explanation

To create the confidence interval either the sample size should be$30$ or more or the population must be distributed normal which means that it should not contain the severe values.

In this case, it would not be possible to make the confidence interval using the stem-plot that contains the outliers.

Hence, the correct option is (c).