MA215 Grantham Constructing Confidence Intervals Discussion

Constructing Confidence Intervals

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  • What is a confidence interval?
  • Why are there two numbers in a confidence interval?
  • Go into the W5 Lecture 2 Notation and Symbols area. Find the two formulas for the “Interval Estimate of the Population Mean.” You will be using one of these, and your job is to pick the right one. What does each variable mean? How are these formulas different? In other words, how do you know when to use each one?
  • 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 – and this statement is SUPER IMPORTANT!!! Why?).
  • 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.
  • To summarize, what “rules” can you make for the behavior of confidence intervals given the three that you calculated?

Hint from Dr. Klotz: Here is my favorite online z sub alpha over two calculator: Keep it handy even after the post.

http://simulation-math.com/_Statistics/FindZalphaover2.cshtml

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