## Week 4 Understanding Confidence Intervals Video Discussion

Question Description

Constructing Confidence Intervals 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 ? = 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. This is my work from week 4: Sampling a pair of die discussion question. One die has six possible outcomes when it is rolled; while two die has 6^2 = 36 possible outcomes when rolled together. Rolling the die ten times produces a 6^10 possible outcomes. Rolling it 20 times produces a 6^20 possible outcomes. Outcomes for the first ten rolls of a die First, die Second, die sum 4 6 10 3 1 4 5 2 7 3 5 8 5 4 9 5 2 7 1 2 3 6 1 7 2 5 7 2 4 6 Total = 68 Average = sum/number of rolls = 68/10 = 6.8 Outcomes for the second 20 rolls of a die First, die Second, die sum 3 2 5 4 6 10 5 6 11 5 6 11 2 2 4 1 3 4 5 5 10 2 6 8 1 4 5 5 5 10 3 6 9 1 2 3 2 2 4 6 5 11 3 5 8 2 2 4 3 3 6 2 5 7 6 4 10 1 1 2 Total = 142 Average = sum/number of rolls = 142/20 = 7.1 A central limit theorem is a theorem which allows us to work with approximately normal distribution by simplifying problems in statistics (Rosenblatt, 1956). The central limit theorem states that the average of a sample distribution approaches normal distribution average as the size of the sample increases. It says that in a test of rolling a die, as the number of rolling a die increases the average of a distribution sample tends to be a normal distribution. While testing the rolling of a pair of die, Ive determined that the average of rolling a die is 7. These results show that when the number of rolling a die increases, the average leans towards seven thus proving the central limit theorem.

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