Question

According to the US Bureau of Labor Statistics publication News, self-employed persons with home-based businesses work a mean of 23 hours per week at home with 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. d. What effect has increasing the sample size on the mean and standard deviation of all possible sample mean hours worked per week at home

Answer 1

Answer:

The answer is below

Step-by-step explanation:

Given that mean (μ) = 23 hours, standard deviation (σ) = 10 hours

a) The population is a group of self employed home based workers while the variable is the number of hours worked per week.

b) The mean of the distribution of sample means (also known as the Expected value of M) is equal to the population mean μ.

$\mu_x=\mu=23\ hours$

The standard deviation of the distribution of sample means is called the Standard Error of M, it is given by:

$\sigma_x=\sigma/\sqrt{n} =\frac{10}{\sqrt{100} }=1$

c) $\mu_x=\mu=23\ hours$

$\sigma_x=\sigma/\sqrt{n} =\frac{10}{\sqrt{1000} }=0.32$

d) The sample size has no effect on the mean, hence increasing the sample size does not change the mean.

The square root of sample size is inversely proportional to the standard deviation therefore increasing the sample size reduces the standard deviation.