Q 8.119. - Elementary Statistics

Question

A simple random sample of size $100$ is taken from a population with an unknown standard deviation. A normal probability plot of the data displays significant curvature but no outliers. Can you reasonably apply the $t-$interval procedure? Explain your answer.

Step-by-Step Solution

Answer

Yes.

Step 1: Given information

From a population with an unknown standard deviation, a simple random sample of size $100$ is taken.

Step 2: Concept

The $t-$interval procedure will be used.

Step 3: Explanation

In this scenario, we may use the $t-$interval approach to determine the confidence interval of the population mean. 

The sample size is $n=100$ here. As the sample size is more than $30$, it is a large sample. The population standard deviation $\sigma$ is unknown.

Significant curvature can be seen in the normal probability plot. The population is therefore not normal; yet, because the sample is big, the sample mean $\overline{x}$ follows a normal distribution independent of the population distribution. In addition, the sample data contains no outliers. Unless the data contains outliers, the $t-$interval technique can be used for large samples. The employment of the $t-$interval technique is therefore justified.