The Sampling Distribution of the Sample Mean

1. Two very important topics that you should carefully reflect upon this week include sampling error and standard error.
(a) Compare and contrast sampling error and standard error. Your discussion must clearly emphasize the distinction between these two topics.
(b) Discuss how sampling error and standard error might arise within the context of an original real-world application.
(c) In what ways (if any) does changing sample size influence sampling error and standard error?

2. The focus of this week is on discussing the sampling distribution of the sample mean. Suppose that the population of interest consists of the five starting players on a men’s basketball team, who we will call A, B, C, D, and E. Further suppose that the numerical continuous variable ( x ) of interest is height, in inches. Although you are required to use different numbers for this discussion, here is an example to provide a framework of what I am looking for of the following requirements: Week 10 DB Exemplar Example __ Distribution of Sample Means.pdf
Actions

(a) Create a table like the one below which shows the height, in inches, of the five starting players.

Player
A
B
C
D
E

Height (Inches)

(b) Discuss how one would obtain a distribution of sample means for this continuous random variable x involving a sample size of 2. Visualize that you were actually going out in-the-field to collect data so that it an be used to create this distribution of sample means. Create a table and determine the sample mean ( ) for each sample of size 2. Fill in two heights for each sample. Determine the sample mean for each sample of size 2. Express each result to the nearest tenths place.

Sample
Heights (Inches)
(Inches)

A , B

A , C

A , D

A , E

B , C

B , D

B , E

C , D

C , E

D, E

(c) Determine the mean for this distribution of sample means ( ). Show all of your work. Discuss how can be used to make informed decisions regarding the population mean . Express your result to the nearest tenths place.
(d) Determine the standard deviation of this distribution of sample means ( ). Show all work. Discuss how can be used to make informed decisions regarding the population standard deviation . Express your result to the nearest tenths place.
(e) Discuss the influence of sample size n over the shape of the distribution of sample means. As you increases sample size, how does it influence this shape?
(f) Within the context of your provided example, discuss the relevance of the Central Limit Theorem in making informed decisions.