Q 8.34 - 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 variable under consideration is very close to being normally distributed, and the sample size is $10$ .

Step-by-Step Solution

Answer

The use of the 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 $10$.

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

Here sample size is $10<15$, the sample size is small and variable is very close to normal distribution.

The procedure to get confidence interval for population mean is reasonable.