Question

pictured below (in scrambled order) are three histograms. one of them represents a population distribution. the other two are sampling distributions of x - bar: one for sample size n = 5 and one for sample size n = 40. based on the histograms, what is the most likely value of the population mean? a. 0; b. 20; c. 5; d. 8

Explanation:

Step1: Recall sampling - distribution property

The sampling - distribution of the sample mean $\bar{x}$ has a mean equal to the population mean $\mu$. As the sample size $n$ increases, the sampling - distribution of $\bar{x}$ becomes more concentrated around the population mean.

Step2: Identify the sampling - distribution with larger $n$

The sampling - distribution with sample size $n = 40$ will be more bell - shaped and more concentrated around the population mean compared to the sampling - distribution with $n=5$. Among the three histograms, the one that is more bell - shaped and concentrated is likely the sampling - distribution with $n = 40$.

Step3: Estimate the population mean

For a normal or approximately normal distribution (the more concentrated histogram), the population mean is approximately at the center of the distribution. Looking at the more concentrated histogram (which is likely the $n = 40$ sampling - distribution), the center is around 8.

Answer:

D. 8