According to the Bureau of Labor Statistics publication...

According to the Bureau of Labor Statistics publication News, self-employed persons with home-based businesses work a mean of 25.4 hours per week at home. Assume a standard deviation of 10 hours. a. Identify the population and variable. b. For samples of size $100,$ find the mean and standard deviation of all possible sample mean hours worked per week at home. c. Repeat part (b) for samples of size $1000 .$

According to the Bureau of Labor Statistics publication News, self-employed persons with home-based businesses work a mean of 25.4 hours per week at home. Assume a standard deviation of 10 hours.
a. Identify the population and variable.
b. For samples of size $100,$ find the mean and standard deviation of all possible sample mean hours worked per week at home.
c. Repeat part (b) for samples of size $1000 .$

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Key Concepts

Population

A population is the entire collection of individuals or items that share a particular characteristic of interest. In statistics, it is the complete set from which samples are taken and about which conclusions are made.

Variable

A variable is a measurable characteristic that can vary among individuals in a population. It represents the data collected on each subject, such as the number of hours worked per week in a home-based business.

Sampling Distribution of the Sample Mean

This is the probability distribution of the means of many independent samples of a fixed size taken from the population. It has a mean equal to the population mean and a standard deviation (known as the standard error) that is equal to the population standard deviation divided by the square root of the sample size.

Central Limit Theorem

The Central Limit Theorem states that, regardless of the population's distribution shape, the distribution of the sample means will approximate a normal distribution as the sample size becomes larger, provided the samples are independent.

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