Q 8.36 - Elementary Statistics

Question

Assume that the population standard deviation is known and decide weather use of the $z$-interval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answers.

The sample data contain outliers, and the sample size is $20$.

Step-by-Step Solution

Answer

The use of the $z$-interval procedure to obtain a confidence interval for the population mean is not reasonable.

Step 1: Given Information

Sample size is $20$ and data contains outliers.

Step 2: Conditions to use z interval procedure

The condition are: 

• Small Sample Size: When sample size is  $n<15$, procedure is used if the variable is normally distributed and very close to being normally distributed.
• Moderate Sample Size: When sample size is between $15-30$, the variable is far from being normally distributed and no outlier in the data. 
• Large Sample Size: When the sample size is greater than $30$, it is used without restrictions. 

Step 3: Explanation

As per the given data and conditions, the use of $z$ interval to obtain confidence interval for the population mean is not reasonable. This is due to the fact that sample data contain outliers.