# What is a confidence interval?

• What is a confidence interval?
• Let’s say you made a confidence interval for a mean taken from the sample that is representative of the population. Will that confidence interval  apply to the population or to the sample?
• 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 s = 2.41).
• What do you notice about the RANGE of the interval for the mean of 10 rolls versus the mean of 20 rolls?  Finish this rule:  As the samples size increases, the range of the confidence interval ______________ (increases/decreases – pick one).
• Using your mean for 20 rolls, calculate the 90% confidence interval.  Compare the range of the confidence interval for 90% to 95%.  Finish this rule:  As the confidence level increases, the range of the confidence interval _______ (increases/decreases – pick one).
• In the project for this week, you are calculating confidence intervals for someone who is picking between the engineering major and the business major.  You are trying to tell him/her what is likely to happen.  Is it more helpful to have a large range or a narrow range in a confidence interval? Why

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