Q 8.39 - 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 sample size is $250$, and the variable under consideration is far from being normally distributed.

Step-by-Step Solution

Answer

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

Step 1: Given Information

It is given that sample size is $250$ and  the variable under consideration is far from being normally distributed.

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

Central limit theorem states that sampling distribution of sample mean is approximately referred to as normally distributed as the sample size is $250$ (large).

Also, variable taken is far from being normally distributed and also the sample data contains no outliers. 

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