Spring 2003
Statistics 515 - Statistical Methods I
Monday/Wednesday 2:30-3:45
210A LeConte

Course Website: http://www.stat.sc.edu/~habing/courses/515S03.html

Practice 3Answers Posted: Thursday, May 1st
(Click here to see them!)
  • Pg 714: 13.15a by hand OR SAS. Also state the null and alternate hypothesis in terms of the parameters and the problem, and check the assumptions.
  • Pg. 732: 13.35 b-d by hand and by SAS. Is the sample size large enough? Is this a test of homogeneity or of independence? Why?
10Due: Wednesday, April 16
  • Page 522: 11.13c, also calculate the SSE, MSE, and a 95% confidence interval for the slope.
  • Page 526: 11.19 using SAS. Also, check that the assumptions for performing regression are met, conduct a test of the null hypothesis that beta_1=0, and construct a confidence interval for the slope.
  • Page 548: 11.54 (both what r and r2 tell us)
9Due: Monday, April 14
  • Page 459: 10.18 a, b, c
  • Page 461: 10.24 a Use SAS to generate your own output and check the assumptions
8Due: Wednesday, April 2
  • Page 405: 9.32
  • Page 365: 8.76
  • Sketch two sample power curves (on the same graph) for testing H0: mu=0 vs. HA: mu < 0 for alpha=0.10. Make one of the curves for a large sample size and the other is for a small sample size. (Be sure and label them!)
Practice 2 Answers posted:
Friday, March 21
(Click here to see them!)
  • Pg. 352: 8.57
  • Pg. 357: 8.62
  • Pg. 370: 8.88
  • Pg. 392: 9.10
  • Pg. 415: 9.51
7Due: Wednesday, March 19
  • Consider the "Scallops, Sampling, and the Law" box write-up and focus questions on page 319. The rule of comparing x-bar to a cut-off could be considered unfair because we don't really want to compare x-bar to the cut-off... we want to compare mu to the cut-off. In this case, what we want is for mu to be at least one for the catch to be legal.
    1. By hand, construct a 95% confidence interval for the mean weight measurement for a bag of shrimp from this boat. (You may use the facts that x-bar=0.9317 and s=0.0753).
    2. Does the catch appear to be legal?
    3. By hand, construct a 95% confidence interval for the standard deviation for the weight measurements for a bag of shrimp from this boat. (Again, you may use the fact that x-bar=0.9317 and s=0.0753).
    4. Use SAS to construct both a 95% CI for the mean and a 95% CI for the standard deviation of the weights of the bags. Remember that whenever you use SAS with your homework you need to include a copy of the code from the Program Editor window and the appropriate part of the output. (The CI for the sd may be slightly different in SAS than by hand.)
    5. Use SAS to construct a Q-Q plot of the observed weights. Does the data seem like it came from a distribution that was very close to normal, somewhat close to normal, or not at all normal?
    6. Based on your answer to e, do you trust the confidence interval you made for the mean to actually be a 95% confidence interval for the mean? do you trust the confidence interval you made for the standard deviation to actually be a 95% confidence interval for the standard deviation?
  • Pg. 313: 7.41 (Show your work!)
  • Pg. 320: 7.54 (Show your work! This one is a lot easier if you've read page 318 and 319)
6Due: Wednesday, March 5
  • Pg. 272: 6.8 and also
    f) Find the sampling distribution of the sample standand deviation s for n=2.
    g) Show that s is a biased estimator for sigma.
  • For n=25 (df=24), find P(t>2.492), P(t<1.318) and P(chi2>33.1963)
  • Page 305: 7.24a
5Due: Wednesday, February 27
    Show your work for any credit!
  • Pg. 248: 5.57 a, also show that n is large enough
  • Pg. 248: 5.62 also show that n is large enough
  • Pg. 279: 6.18
  • Pg. 280: 6.28 a-b, also say why the np, n(1-p) rule doesn't apply
Practice Answers posted:
Friday, February 14
(Click here to see them!)
  • Pg. 186: 4.22 part a only
  • Pg. 201: 4.52, also
    f) What is the probability that the psychic would get exactly two correct if they had no ESP?
    g) What is the probability that the psychic would get exactly two correct if they had ESP with p=0.5?
  • Page 234: 5.16 a,d; 5.20 d; 5.24 c
4Due: Wednesday, February 12
  • Pg. 128: 3.26 begin by writing out the sample space
  • Pg. 167: 3.107 b,c (show your work, beware the book answers!)
  • Pg. 169: 3.116
  • Pg. 170: 3.124 a
3Due: Wednesday, February 5 For this assignment use the data set in problem 2.15 on page 29. (The dataset can be found on the CD that came with the book.)
  1. Using SAS calculate the mean, median, and standard deviation of this data set. (Remember to include a copy of the code you ran and the output.)
  2. In general, would the mean or median be more useful for getting an idea of how much oil is spilled in a typical accident? Why?
  3. Would you classify any of the reported spillage amounts as outliers? Why or why not? (e.g. What rule did you use?)
  4. Use SAS to construct a Q-Q plot for this data. Does the data appear to follow a normal curve for the most part?
  5. Count the number of measurements in the intervals mean +/- s, mean +/- 2s, and mean +/- 3s, and convert these raw counts into percentages.
  6. Compare the percentages found in 5 to the Empirical Rule and Chebyshev's rule. Does this seem reasonable in light of your conclusion in part 4?
2Due: Wednesday, January 29
  1. Pg. 59: 2.56b (Show all your work.)
  2. Consider the data in problem 2.56b on page 59.
    a) Find the mean, median, standard deviation and variance if each number in the data set is multiplied by 2.
    b) Find the mean, median, standard deviation and variance if each number in the data set has 2 added to it.
    c) Write down a general rule about the effect on the mean, median, standard deviation, and variance when the data is multiplied by a constant.
    d) Write down a general rule about the effect on the mean, median, standard deviation, and variance when the data has a constant added to it.
  3. Pg. 68: 2.75, explain how you got your answers!
1Due: Wednesday, January 22
  1. Read page 15, and consider the AAUW study at the bottom concerning the happiness of high school girls.
    a) Is the response of each girl to the question qualitative or quantitative?
    b) What is misleading about saying that "only 29% of high school girls" are happy with themselves? (Hint: What does it imply about the other 71% and why isn't this true?)
    c) The AAUW compared the high school girls to elementary school girls. Think of another group that they could be compared to and argue (in a sentence or two) why your choice might be better.
    d) Why does it seem unreasonable that this is truly a random sample as defined on page 12. (Hint: What would you need to have in order to choose such a random sample).
  2. Consider the data in 2.21 (pg. 38)
    a) If you were to make a histogram for this data set, why would it be somewhat misleading to combine the first two classes into a single class from 0.0 to 0.9? (I mean, the others are all one long, why not this one?)
    b) Say the bar for the class 1.0-1.9 was drawn to go from 0.95 to 1.95 and was 5.8 units high. Similarly the bar for for the class 2.0-2.9 went from 1.95 to 2.95 and was 30.8 units high. Describe the bars for the separate classes 0 and 0.1-0.9, and also the bar that the joined class would have.
  3. For the data in 2.56b (pg.59) calculate the mean, median, and mode. Is this data set skewed (if so, in which direction) or symmetric?