MA 215 UAG Statistics Confidence Interval Discussion Questions

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funjglq

Mathematics

University of Arkansas Grantham

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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 ? = 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.

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)

Explanation & Answer:
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Explanation & Answer

Answer: In inferential statistics, observed sample data is used to estimate population.

A confidence interval shows us the estimated value of range, to include the parameter for an unknown population which is being calculated from a given set of sample data using the sample size, mean, standard deviation and confidence interval. There are actually factors that directly affect the size of the confidence interval for a specific confidence level. These are the sample size, population size and the percentage. In the previous discussion (week 4), a pair of dice was rolled 10 times and the average sum of the rolls were calculated. Afterwards, the same procedure was don...


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