Q 8.35 - 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 $75$.

Step-by-Step Solution

Answer

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

Step 1: Given Information

It is given that sample size is $75$.

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, the sample size is $75>\left(30\right)$, sample size is large.

The use of $z$ interval procedure to get confidence interval for population mean is reasonable.