Section: Module 5: Lesson 3: The Central Limit Theorem | Intro to Statistics | NextGenU.org

  • Student Learning Outcomes:
    Upon completion of this lesson, you will be able to:
    • Explain the Central Limit Theorem (CLT) and its importance in Inferential Statistics.
    • Find and apply the mean and standard error of the sampling distribution of the mean, as summarized by the CLT.
    Approximate time required for the readings for this lesson (at 144 words/minute): 3 hours and 35 minutes.

    Click here to start this lesson

    • Required Learning Resources and Activities
    • url icon
      The Central Limit Theorem URL
      Students must
      View

      Watch entire Video. (10 minutes)

      Khan Academy - 2022

    • url icon
      Sampling Distribution of the Sample Mean, x-bar URL
      Students must
      View

      Read entire page. (20 minutes)

      Florida state University - 2022

    • forum icon
      Practical Activity 4 Forum
      Students must
      View
      Start discussions: 1

      Student Learning Outcome (Module 5 Lesson 3): Find and apply the mean and standard error of the sampling distribution of the mean, as summarized by the Central Limit Theorem.

      Step 1. Review

      Review the learning resources for this lesson before studying the case problem.

      Step 2. Analyze

      Analyze the case problem below.

      Part 1:

      Use the set of numbers {10, 20, 30, 40, 50} to perform he following tasks:

      1. Make a list of all possible samples of size 2 that could be drawn with replacement from this set of numbers, for example, (20, 30), (10, 50), (40, 40).
      2. Find all the sample means and construct the sampling distribution of sample means in tabular form, an example of which is shown below.

      82

      3. Find all the sample ranges and construct the sampling distribution of sample ranges in tabular form, an example of which is shown below.

      22

      Part 2:

      4. Using the Central Limit Theorem, calculate the mean and standard error of the sampling distribution of sample means.

      Step 3. Respond

      Respond to the case problem by writing answers to Questions 1, 2, 3, and 4.

      Step 4. Share

      To share your work, access to the first post below and click on the “Reply” button under this post and paste your work into the “Message” box. Make sure to reference others’ intellectual property when necessary. All references should follow 7th Edition APA formatting. For further instructions, see the resource on the Himmelfarb Health Sciences Library: APA citation resource (N.B. references are excluded from word counts).

      Step 5: Interact

      To complete the activity, you will need to reply to at least two posts by your peers respectfully and professionally. Ensure that your post engages your peers' ideas by including a reflection on their comments, sharing ideas of other potential difficulties and parties involved, or asking thought-provoking questions. If a peer comments on your posting, please reply. To post a reply, click “Reply” on a particular discussion, write your feedback and then click on “post to the forum.”

      OPTIONAL Step 6: Interact (10 minutes)

      If you would like to, you can reply to your peers' posts in a respectful and professional manner. Ensure that your post engages your peers' ideas by including a reflection on their comments, sharing ideas of other potential difficulties and parties involved, or asking thought-provoking questions. If a peer comments on your posting, please reply. To post a reply, click “Reply” on a particular discussion, write your feedback and then click on “Post to forum.”


    • quiz icon
      Quiz: Module 5

      To access the quiz, click on the name of the quiz provided above. On the following screen, click the attempt quiz button to respond to the questions.

      TO PASS THIS QUIZ YOU MUST OBTAIN A SCORE OF 80%.

      Not available unless: The activity Quiz: Module 4 is marked complete