Week 9 Current Topics, Readings, and Exercises for Introduction to Statistics

MATH 117 Online Statistics
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The information about the current topics, readings, and exercises for which you are responsible will be posted on this page. (Information about topics, readings, and exercises for previous weeks can be accessed at the bottom of this page.)

Please remember that the only way in which to learn the material is to do the readings and practice exercises. The readings and practice exercises document does not have any dates, however, each section is listed, in general, in the order in which the material will be covered throughout the semester. The current topics, readings (text, PowerPoints, online), and corresponding exercises for which you are responsible will be listed below each week. Once sections and readings have been assigned, you are expected to read the sections and to work on the corresponding/related practice exercises. You MUST use the MyMathLab as well. The resources on MyMathLab include preparation discussions, PowerPoint slides, data files for the exercises, Statlets (applets for Statistics), video lectures and other resources for each chapter such as practice quizzes, practice tests, and hints and similar exercises facilities for use when working on practice exercises.

Current Topics, Readings (text, PowerPoints, online), and Exercises on which you should work during Week 9:

In Module7:
- Read Chapter 9 and do all practice exercises for Chapter 9
- Do the Chapter 9 Review exercises
- Review the PowerPoint on the PowerPoint Class-Notes page:
  - Confidence Intervals
- Do the online readings for Chapter 9
  - Confidence Intervals (online glossary)
  - Confidence Intervals (includes applet)
  - Confidence Intervals – Select “Estimation” and then “Confidence Intervals” on the Table of Contents
  - Confidence Interval for a Population Proportion
  - Confidence Intervals: Confident Interval, Single Population Mean, Standard Deviation Known, Normal
  - Confidence Intervals: Confidence Interval, Single Population Mean, Standard Deviation Unknown, Student-t
- Watch the corresponding video lectures and view the associated PowerPoints and materials on MyMathLab/MyStatLab for Chapter 9

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Explore sampling distributions using the Sampling Distribution applet.
- General Information about the Applet:
  - Read the general information on the main page as well as the information below.
  - Select a distribution type: For this applet, you may select a normal, uniform, skewed, or custom parent population.
  - Select a sample size: From the parent population, you may select samples of size N = 2, 5, 10, 16, 20, or 25.
  - Select a statistic: For this exploration, you will select the Mean as the statistic since you will explore the sampling distribution for the mean. The top pull-down menu to the right of the Distribution of Means graph is used to select the statistic and the lower pull-down menu is used to select the sample size, N.
  - Explore the sampling distribution for the mean:
    - Using the Animated button: You may view one sample of size N selected from the parent population and it corresponding mean. The histogram for the sample will be displayed in the sample data graph and the histogram for the distribution of the means will be displayed in the distribution of the means graph. The Animated button generates one sample and its corresponding mean at a time. The mean for each sample remains in the distribution for the means graph until you left-click the Clear lower 3 button; the Clear lower 3 button clears the three graphs below the graph for the parent population.
    - Using the 5, 1,000, or 10,000 button: You may generate 5 repetitions, 1,000 repetitions, or 10,000 repetitions for the generation of samples of size N at a time using the 5, 1,000, or 10,000 button. If you have generated any individual samples then the newly generated sample means will be added to the distribution of the means graph. When you use the 5, 1,000, or 10,000 buttons, the sample data is not displayed in the sample data graph.
- Use the Applet: Left-click the Begin button and follow the directions below.
  - Get a feel for the situation: For a Uniform parent population, select the sample size N = 2 using the pull-down menu to the right of the Distribution for Mean graph and left-click the Animated button: observe the histogram for the sample of size N = 2 generated in the sample data graph and the mean of these values displayed in the Distribution of Mean graph. Repeat this several times, observing that each subsequent mean is added to the Distribution for Mean graph. Repeat for N = 5, 10, 16, 20, and 25. Note: The graphs are cleared when you change the sample size. Repeat the process above for Skewed and Normal parent distributions. Use the custom entry to create bimodal and multimodal distributions (left-click and drag the cursor in the parent population graph to "paint" the distribution with the mouse) and repeat the process for these distributions.
  - For parent populations that are Uniform, Skewed, Normal, Bimodal, and Multimodal and for sample sizes N = 2, 5, 10, 16, 20, and 25,
    - use the 5 button to generate 5 samples of size N at a time. Monitor the histogram and the mean of the distribution of the means.
      - as the number of repetitions increases, classify the Distribution of the Means and compare the mean of the Distribution of the means to the mean of the parent population.
      - As the number of repetitions increases, what is the classification of the Distribution of the Means?
      - As the number of repetitions increases, what is the relationship between the mean of the Distribution of the Means and the mean of the parent distribution?
    - use the 1,000 button to generate 1,000 samples of size N at a time. Monitor the histogram and the mean of the distribution of the means.
      - as the number of repetitions increases, classify the Distribution of the Means and compare the mean of the Distribution of the means to the mean of the parent population.
      - As the number of repetitions increases, what is the classification of the Distribution of the Means?
      - As the number of repetitions increases, what is the relationship between the mean of the Distribution of the Means and the mean of the parent distribution?
    - use the 10,000 button to generate 10,000 samples of size N at a time. Monitor the histogram and the mean of the distribution of the means.
      - as the number of repetitions increases, classify the Distribution of the Means and compare the mean of the Distribution of the means to the mean of the parent population.
      - As the number of repetitions increases, what is the classification of the Distribution of the Means?
      - As the number of repetitions increases, what is the relationship between the mean of the Distribution of the Means and the mean of the parent distribution?
  - Based on these explorations, what conclusion can you draw about the classification of the Distribution of the Means? Does this agree with the Central Limit Theorem?
  - Based on these explorations, what conclusion can you draw about the relationship between the mean of the Distribution of the Means and the mean of the parent population? Does this agree with the Central Limit Theorem?

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Topics, Readings, and Exercises from previous weeks: Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8

Please remember that your questions are important to me, that I want to help you to do well in the course, and that there is no such thing as a stupid question.

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This site was created and is maintained by Sarah L. Mabrouk, Mathematics Department, Framingham State College. If you notice any broken hyperlinks, please feel free to send email.