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Question Description

  • Sampling with a Pair of Dice

    Go to the link: http://www.random.org/dice/

    • Roll the 2 virtual dice and calculate the sum of the pair of virtual dice. Do this 10 times.
    • Then after you have rolled the virtual pair dice 10 times and calculated 10 sums calculate the average of these 10 sums.
    • Conduct this experiment again but this time roll the virtual pair of dice 20 times and calculate the 20 sums and then find the average of these 20 sums.
    • Discuss the Central Limit Theorem. What is it? What does it say? Summarize it in your own words.
    • Post your results and discuss how the dice activity relates to this week’s lesson, particularly the Central Limit Theorem.
    • Constructing Confidence Intervals

      • What is a confidence interval? What information do confidence intervals give you?
      • What advantages do confidence intervals give over a single number?
      • How do you compute a confidence interval?
      • Why do confidence intervals have two numbers? What does each represent?
      • In the discussion for week 4, you rolled a pair of dice 10 times and calculated the average sum of your rolls. Then you did the same thing with 20 rolls. Use your results from the week 4 discussion for the average of 10 rolls and for the average of 20 rolls to construct a confidence interval for the true mean of the sum of a pair of dice (assume σ = 2.41, and you are doing a 95% confidence interval).
      • What do you notice about the length of the interval for the mean of 10 rolls versus the mean of 20 rolls? Did you expect this? Why or why not?
      • What would happen to the length of the interval if the confidence level was 99% instead of 95%? Why? What if it were a 90% confidence interval?
      • Errors in Hypothesis Testing

        • What is hypothesis testing? What are you trying to find out?
        • What are the steps in hypothesis testing?
        • What is a null hypothesis, and why is it important to hypothesis testing?
        • Now consider the situation where a husband and wife go to the doctor’s office to each get some tests run and the doctor accidently mixes up their charts. The doctor comes into the exam room with the results of the tests and declares that the wife is NOT pregnant but her husband IS indeed pregnant with a baby. In section 9.2, the concepts of Type I and Type II errors are introduced.
        • How does this scenario illustrate the concepts behind Type I and Type II errors?
        • With this situation in mind, what type of error (Type I or Type II) is worse? Explain your reasoning.
        • Remember to focus on the statistical concepts (rather than biological concepts) in this posting. The post's focus is on the error types and not whether or not men can have babies.
      • Relationship of Height and Weight

        • What is regression analysis?
        • In every-day language, what is a trendline, and what is it telling us?
        • What does it mean to interpolate? What does it mean to extrapolate?
        • Using the given Height and Weight data set, follow the steps in the weekly video or on pages 584-585 of the textbook for performing a regression analysis using Excel to analyze the Height and Weight Data set (assume height is the input variable x and weight is the output variable y).
        • Once you have performed the analysis in Excel, state the correct simple linear regression equation and use the regression equation to predict the weight (in pounds) of a person who is 65 inches tall and the weight (in pounds) of a person who is 100 inches tall.
        • Why might the regression equation you have found not be a good predication of the weight of someone who is 100 inches tall? Are you interpolating or extrapolating when you use the trendline to predict the weight?

        Download the Height and Weight Table Here.

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