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$20$.

Short answer

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

Step-by-step solution

Given Information

Sample size is $20$and data contains outliers.

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.

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.