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
(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.
NOTE: Although students will be casting their response within the context of the same real-world example, the heights of the players and results must be different than the other students. You will receive no credit for your work if you use the same heights or arrive a the same numerical results as other students.
All responses must be original. If you provide the same response as one of your other classmates or copy/paste information from other sources, you will receive no credit for your post.
All work must be typed within the provided discussion board fields. Do not submit attached Word files containing your response to any component of this discussion. No credit can be given for any photographed handwritten work that is submitted to the discussions.
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