Week 4 Understanding Confidence Intervals Video Discussion

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 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.