Fall 2003
Statistics 515 - Statistical Methods I
Monday/Wednesday 4:00-5:15
113 LeConte

Course Website: http://www.stat.sc.edu/~habing/courses/515F03.html

Practice 3Answers posted
Tuesday, December 9th
  • 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?
Practice 2Answers posted
Saturday, November 22nd
  • Page 522: 11.13c, also calculate the SSE and the MSE.
  • 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 verify that the degrees of freedom in the ANOVA table are correct.
  • Page 548: 11.55b. That is, describe the relationship between exposure time and goodness of view.
9Due: Wednesday, November 19th
  • Page 459: 10.18 a,b,c
  • Page 461: 10.25 b-d. Generate your own SAS output. and check the assumptions.
8Due: Wednesday, November 12th
  • Page 393: 9.13 Construct the confidence interval in part a by hand, assuming the variances are equal. Use SAS to calculate the means and variances for part a and to do part b.
  • also, c) By hand AND using SAS, conduct a test of the hypothesis that the two groups have the same mean against the alternate hypothesis that the group means are different using alpha=0.05 and the result you found in part b concerning the variances.
  • Page 416: 9.51
7Due: Monday, October 27th
  • Pg. 339: 8.27a (note the mean and SD are given on pg. 340). Also test H0: sigma2=1 vs. HA: sigma2>1 by hand. Finally, describe how you would check if the assumptions for these tests are met, and how closely they need to hold for each one.
  • Pg. 357: 8.62
6Due: Wednesday, October 22nd
  • 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: 7.38 a,b (Use the Agresti and Coull correction and show your work!)
  • Pg. 320: 7.54 (Show your work! This one is a lot easier if you've read page 318 and 319)
5Due: Wednesday, October 15th
  • Pg. 272: 6.8 and also
    f) Would s2 be unbiased for sigma2 if we divided by n instead of n-1?
  • For n=14 (df=13), find P(t<3.012), P(chi2>22.3621), and t0 such that P(-t0 < t < t0)=0.95
4Due: Monday, October 6th
  • Pg. 234: 5.16a,c; 5.20c; 5.24d
  • Pg. 248: 5.57c Show your work and that n is large enough
  • Pg. 280: 6.28a-b Also say why the np, n(1-p) rule does not apply.
Practice Answers posted
Monday, September 22nd
  • Pg. 170: 3.124a
  • Pg. 186: 4.22a
  • 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?
3Due: Wednesday, September 17th
  • Page 60: 2.61, show your work
  • Page 68: 2.75, explain how you got your answers
  • Page 117: 3.6
  • Page 147: 3.62, also
    c) What is P(A intersect B), P(A|B), and P(A U B) if A and B are mutually exclusive.
2Due: Wednesday, September 10th For this assignment use the data set in problem 2.100 on page 84. (A copy of the data set is on the disk that came with your text book. Remember to include a copy of the code you ran, and any output you refer to with your answers.)
  1. Using SAS calculate the mean, median, and standard deviation of this data set.
  2. In general, would the mean or median be more useful for getting an idea of how much a new graduate would be paid in a given field? Why?
  3. Would you classify any of the reported salaries as outliers? Why or why not?
  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?
1Due: Wednesday, September 3rd
  • Page 17: 1.26 also justify your answer to part d
  • Page 53: 2.48 b-c
    also construct a historgram for this data
    is it skewed? which direction?