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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.

**Note below are the average sum of my rolls from my discussion for week 4. This information is needed to help answer question above.**

When rolling the dice 10 times, the results are shown below:

3+2=5
5+5=10
1+1=2
1+5=6
3+6=9
4+1=5
1+1=2
2+6=8
1+5=6
3+2=5
(Total avg: 58/10=5.8)

When rolling the dice 20 times, the results were as shown below:

1+2=3
1+3=4
6+4=10
2+1=3
6+1=7
1+3=4
6+5=11
1+6=7
1+2=3
4+1=5
6+2=8
2+2=4
3+2=5
3+3=6
1+6=7
5+2=7
2+1=3
3+3=6
2+2=4
1+5=6
(Total avg: 113/20=5.65)

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