Q 8.37 - 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 no outliers, the variable under consideration is roughly normally distributed, and the sample size is $20$.

Step-by-Step Solution

Answer

The $z$-interval procedure to obtain a confidence interval for the population mean is reasonable. 

Step 1: Given Information

The variable under consideration is roughly normally distributed. The sample data contains no outliers.

Step 2: Conditions to use z interval procedure

The conditions 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

Sample size is $20$.

It lies between $15-30$.

Therefore, $z$ interval procedure to obtain a confidence interval for the population mean is reasonable.