Sample Exam Questions

Regnova Sp 2002

 

Jargon and Basics

  1. What is the difference between a discrete distribution and a continuous distribution?  Give an example of each.
  2. How are the sample space and probability related?
  3. What is a random variable?

Binomial

  1. What is the difference between a combination and a permutation?

Central Tendency & Variability

  1. Define the mean, median and mode.
  2. Give a concrete example of a distribution where the median would be preferred to the mean.
  3. What happens to the mean, median, and mode when the distribution becomes skewed?  Draw a picture to illustrate your answer.
  4. Define the range, variance, and standard deviation.
  5. What is a z score?
  6. What is the implication of Tchebycheff’s inequality?

 

Sampling Distributions and Point Estimation

  1. What are the two meanings of term ‘parameter’ according to Hays?
  2. What is a sampling distribution?
  3. What is the standard error?
  4. What is the principle of maximum likelihood?
  5. What is bias (in the statistical sense)?
  6. What is a confidence interval?

Normal Distribution

  1. What are the parameters that drive the normal distribution?  What does each control?  Draw a picture to illustrate your answer.
  2. About what percent of observations fall above the mean of a normal distribution?  About what percent fall between plus and minus 1, 2 and 3 standard deviations from the mean?
  3. What is the central limit theorem?
  4. Why is the number 1.96 such a big deal for the normal distribution?
  5. Describe the standard error of the mean, , when samples are drawn from a normal distribution.  What determines its size?

Hypothesis Testing

  1. What is a statistical hypothesis?
  2. Why is the null hypothesis so important?
  3. What is a rejection region?
  4. What does it mean to say that a finding is statistically significant?
  5. Describe Type I and Type II errors.  Illustrate with a concrete example.
  6. Describe a situation in which Type II errors are more serious than are Type I errors (and vice versa).
  7. What is statistical power?  Why is it important?
  8. What are the main factors that influence power?
  9. What can you do with Bayes theorem?  Why might it be useful?

The t-test

  1. How are the distributions of z and t related? 
  2. Given that , construct a rejection region.  Draw a picture to illustrate.
  3. What is the standard error of the difference between means?  What are the factors that influence its size?
  4. What are the main uses of the t-test?
  5. Give a concrete example of the use of the {one sample, independent samples, dependent samples} t-test.  State why the particular test is the right one to choose.
  6. What is the importance of variance accounted for?

Chi-square & F

  1.   Describe the chi-square distribution.  What is it made of?  What affects its shape?
  2. What are the mean and variance of the chi-square distribution?
  3. Suppose N=15 and s2 is 10.  Then df=14 and for Q=.025 the value is 26.12.  For Q=.975 the value is 5.63.  What are the limits of the 95 percent confidence interval for ?
  4. Describe the F distribution.  What is it made of?  What affects its shape?
  5. How is the t distribution related to the F distribution?