Question

Barron's reported that the average number of weeks an individual is unemployed is 17.5 weeks. Assume that, for the population of all unemployed individuals, the population mean length of unemployment is 17.5 weeks and that the population standard deviation is four weeks. Suppose you would like to select a sample of 45 unemployed individuals for a follow-up study. Show the sampling distribution of x- the sample mean average for a sample of 45 unemployed individuals.

Answer 1

In this case, the standard error (SE) for the sampling distribution of x is approximately 0.596 weeks.

Step-by-step explanation:

To understand the sampling distribution of x, the sample mean average for a sample of 45 unemployed individuals, we need to consider the characteristics of the population.

Given:

• - Population mean length of unemployment (μ) = 17.5 weeks
• - Population standard deviation (σ) = 4 weeks
• - Sample size (n) = 45

The sampling distribution of x is the distribution of all possible sample means from samples of the same size taken from the population. It follows certain properties, such as:

• 1. The mean of the sampling distribution of x is equal to the population mean: μx = μ = 17.5 weeks.
• 2. The standard deviation of the sampling distribution of x, also known as the standard error (SE), can be calculated using the formula: SE = σ / √n, where σ is the population standard deviation and n is the sample size.

Let's calculate the standard error:

SE = σ / √n

SE = 4 weeks / √45

SE ≈ 0.596 weeks

So, the standard error (SE) for the sampling distribution of x is approximately 0.596 weeks.