Question

A simple random sample of size $17$ is taken from a population with an unknown standard deviation. A normal probability plot of the data reveals an outlier but is otherwise roughly linear. Can you reasonably apply the $t-$interval procedure? Explain your answer.

Short answer

No.

Step-by-step solution

Given information

From a population with an unknown standard deviation, a simple random sample of size $17$ is taken.

Concept

The $t-$interval procedure will be used.

Explanation

In this scenario, we cannot use the $t-$interval technique to get the C.I for the population mean. The sample size is $n=17$, which is considered modest. The normal probability plot also reveals an outlier but is otherwise linear. As a result, we can't utilize the $t-$interval technique because it can't be used with a modest sample size if the data contains outliers. However, if the removal of the outlier is warranted, we can utilize the $t-$interval approach because the normal probability plot following the outlier removal is generally linear.