MA215 DISCUSS

1. Watch this video

https://www.youtube.com/watch?v=rBjft49MAO8

Go to the link:  http://www.random.org/dice/      (or any other online dice rolling link)

· Roll the 2 virtual dice and calculate the sum of the pair of virtual dice.  Do this 10 times.  List your rolls.  Show your calculations.

· Then after you have rolled the virtual pair dice 10 times and calculated 10 sums, calculate the average of these 10 sums.  Show your calculations.

· Conduct this experiment again, but this time roll the virtual pair of dice 20 times. Calculate the 20 sums, and then find the average of these 20 sums.  Show your work.

· How does these exercises relate to this week’s lesson, particularly the Central Limit Theorem?

If we took everyone’s averages for the 20 rolls, and made a histogram, what would we expect to see, and why?

2. Watch this video  https://www.youtube.com/watch?v=tFWsuO9f74o

· What is a confidence interval?

· What are some factors that affect the size of a confidence interval?

· 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 95% confidence interval for the true mean of the sum of a pair of dice (assume σ = 2.41).  

· 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?

· Using your mean for 20 rolls, calculate the 90% confidence interval.  Explain its size as compared to the 95% confidence interval for 20 rolls.

3. Watch the video:  https://www.youtube.com/watch?v=0zZYBALbZgg

· What are the steps in hypothesis testing?

· What is the goal of hypothesis testing?

· What are null and alternative hypotheses?

· In §9.2 the concepts of Type I and Type II errors are introduced.Consider the situation where a husband and wife go to the doctor’s office to each get some tests run and the doctor accidentally 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.

· How does this illustrate the concepts behind Type I and Type II errors?  Make sure to state your null hypothesis for this situation when discussing error.

4. Download the Height and Weight Table Here.

· What does it mean when we say that there is a relationship between two variables?

· What kinds of relationships can there be between two variables?

· Give an example of two variables that are related.  For example, my daughter earns an hourly wage. Her paycheck amount is related to how many hours she worked.

· Give an example of two variables that are NOT related.

· 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? How does this lesson apply to the workplace?