Q 8.38 - 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 distribution of the variable under consideration is highly skewed, and the sample size is $20$ .

Step-by-Step Solution

Answer

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

Step 1: Given Information

Sample size is $20$.

The distribution of the variable under consideration is highly skewed.

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

Since the distribution of the variable under consideration is highly skewed and sample size is $20$, the use of z interval procedure to obtain a confidence interval for the population mean is not reasonable.