K300 Statistics, Prof. Kruschke

Exam 1: Sample Questions
Updated 10:00pm, Monday January 24, 2005

Be sure to
  • write your name and ID on every page
  • write clearly
  • annotate your computations -- an unannotated sequence of numbers and derivations that mysteriously ends up with the correct numerical answer will not be given full credit
  • answer every part of every question.
    1. Basic descriptive statistics. Suppose a sample of scores consists of
      1, 1, 1, 2, 2, 3, 6, 8

      1. Make a histogram (by hand) using bins with upper values of 1, 3, 5, 7 and 9.
      2. What is the mean of the sample?
      3. Suppose the scores were entered in an Excel spreadsheet in cells B3:B10. What would you type in an empty cell to have Excel compute the mean?
      4. What is the median of the sample?
      5. What is the mode of the sample?
      6. Is the sample symmetric or skewed, and if skewed, in which direction?
      7. What is the variance of the sample? Show your work using columns of X, (X-M), (X-M)2.
      8. What is the standard deviation of the sample?
      9. Suppose the scores were entered in an Excel spreadsheet in cells B3:B10. What would you type in an empty cell to have Excel compute the standard deviation? [Careful to use the right version of the command... does it end in "P" or not?]
      10. In this distribution, what is the Z-score of the raw value 1? (That is, convert the raw value 1 to a Z score.)
      11. What would be the "raw" value of a datum whose Z-score is 2.0?
    2. Percentages under normal distributions. Suppose a population of heights is normally distributed.
      1. What is the Z-score of a person at the 16th percentile?
      2. What percentage of people are taller than a person whose Z-score is 2.0?
      3. What percentage of people have heights between Z = -1.96 and Z = +1.96?
    3. Percentages under NON-normal distributions.
      1. Suppose a distribution is severely skewed to the right. Is the percentage of scores from the mean to +1SD equal to 34%? Is the percentage of scores from the mean to +1SD equal to the percentage of scores from the mean to -1SD?
      2. Suppose a distribution is severely kurtotic, that is, it has lots of outliers on both sides of a narrow central peak. Is the percentage of scores from the mean to +1SD greater than, equal to, or less than 34%?
    4. Sampling and probability.
      1. Suppose our class consists of 55 females and 25 males. If we write each student's ID number on a piece of paper and put all the pieces of paper in box and draw one at random such that every ID number has an equal chance of being drawn, then what is the probability of getting an ID belonging to a female?
      2. Suppose a population of scores in normally distributed with a mean of 70 and a SD of 15. If every score is equally likely to be sampled, what is the probability of sampling a score between 70 and 85? What is the probability of sampling a score between 40 and 100?