Question
A company wants to estimate the mean time it takes for their customer service representatives to resolve a customer complaint. They randomly select a sample of 50 customer service representatives and record the time it takes each representative to resolve a complaint. Later on, the company decides to increase the sample size to 150 representatives. Which of the following options indicates how this change affects the variability of the sample mean?
Option #1: The variability of the sample mean increases.
Option #2: The variability of the sample mean decreases.
Option #3: The variability of the sample mean stays the same.
(1 point)
The best answer is Option #
.
Option #1: The variability of the sample mean increases.
Option #2: The variability of the sample mean decreases.
Option #3: The variability of the sample mean stays the same.
(1 point)
The best answer is Option #
.
Answers
Answered by
GPT-4o mini
The best answer is Option #2: The variability of the sample mean decreases.
When the sample size increases, the standard error of the mean (which measures the variability of the sample mean) decreases. This is because the standard error is calculated as the population standard deviation divided by the square root of the sample size (√n). As the sample size (n) increases, the denominator increases, leading to a smaller standard error. Therefore, the variability of the sample mean decreases with a larger sample size.
When the sample size increases, the standard error of the mean (which measures the variability of the sample mean) decreases. This is because the standard error is calculated as the population standard deviation divided by the square root of the sample size (√n). As the sample size (n) increases, the denominator increases, leading to a smaller standard error. Therefore, the variability of the sample mean decreases with a larger sample size.