Confidence Intervals for the Mean

Answers

1. A t distribution has more scores in its tails and fewer in the center than a normal distribution, so it is leptokurtic. Also, a t distribution with 20 degrees of freedom has 95% of its distribution within 2.086 standard deviations of its mean.
   
   
2. As the degrees of freedom increase, the t distribution looks more and more like a normal distribution.
   
   
3. Use the "Find t for a confidence interval" calculator for a 90% confidence interval and you will get 1.753.
   
   
4. Use the "t distribution" calculator and enter 10 for df and 2 for t. You will see that the probability of getting something greater than 2 SDs from the mean is .0734, so the probability of getting something less than 2 SDs from the mean is 1 - .0734 = .9266. 
   
   
5. Use the "t distribution" calculator and enter 10 for df and 2 for t. You will see that the probability of getting something greater than 2 SDs from the mean is .0734, so the probability of getting something less than 2 SDs from the mean is 1 - .0734 = .9266.