Week 4 Understanding Confidence Intervals Video Discussion
Week 4 Understanding Confidence Intervals Video Discussion
Constructing Confidence Intervals
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- 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.
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.