Help

For each student indicate what you think it is about their examples that clarify the concept “mean of the sampling distribution.” The concept is abstract, but how do their examples make it concrete and more understandable? As an alternative, you could explain how the concept of a sampling distribution pertains to inferential statistics.

LC-Student 1

In inferential statistics, sampling distribution refers to the distribution that happens when we find the means of all possible samples of a given size (Bennett et al, 2018). This allows for sampling of smaller sizes to represent a larger population. For example, say you want to find the average weight of an adult male leopard gecko and want to use your 4 pet leopard geckos as the sample size for this experiment. You would weigh each of your adult male leopard geckos, individually; find the average (mean) weight of the 4 lizards.

The mean of the sample size would be found by adding the 4 weights together and taking that sum and dividing it by 4 (the number in the sample size). Example: (weight of lizards in grams) 

That will give you one mean, which in this case isẊ=15.25. You then repeat those steps 20 times. That is, you obtain 20 sets of 4 weights. For each of the 20 sets you compute the mean of weights. You will have 20 means. You will compute the total of each of the 20 samples mean and divide this number by the total number of means computed, (20 in this case). These are a sampling distribution.

References

Bennett, J., Briggs, W.L., & Triola, M.F., (2018). Statistical reasoning for everyday life (5th ed.). Pearson Education, Inc.

SS-Student 2

I think I am following this please feel free to let me know if this is not correct or if I need to tweek anything, thanks.

An example of a real-life scenario in which it would be appropriate to find the sample mean of a sampling distribution would be as follows:

A not-for-profit group receives a surplus of art supplies for daycare centers in their area. In order to evenly distribute these supplies the group would like to know on average how many children are in the centers daily. However, the population parameter is unknown as number of children served daily is only recorded by each individual center.

In order to find the average served daily someone could call each center 200 in all and ask how many children they serve on that day. Which is very time consuming and since that person would have to be paid can be expensive for the group.

Therefore, we would use inferential statistics to estimate the population parameter of number of children served. By using sample distribution of the mean a statistical inference could be made regarding the mean number of children in care for the supplies to be evenly distributed to the centers based on average amount of children served by the centers.

By selecting 20 centers and asking how many children were present on that day and finding the mean number of children in the total of the centers. The population of interest is known as 200 and our sample is 20 (n=20), the average amount of children u (mu) is unknown. This would give us a possible sample size of 200 to the 20th power or 1.048576e+46 which is a super huge number of possible samples. In order to find the sample mean I would have to include all samples so I would most definitely need a computer with the soft ware capability to do so. However, when the sample mean is found for each sample, I would be able to take the mean of the total means and have the mean of the sampling distribution which would be used as the mean for the population parameter.

In this case, I would be able to know the average amount of children in care daily to evenly distribute art supplies to the centers.