Homework

Link to previous assignments.

If you cannot obtain an answer or are unsure of your answer, discuss the problem with each other or with anyone else who might be helpful.

http://www2.ncsu.edu/ncsu/chemistry/resource/t-table.html contains a table of percentage points of Student's t distribution for 80%, 90%, 95%, and 99% and 1 to 30 degrees of freedom (df).  (The first line contains a typographical error: "6.134" should be "6.314".)

http://bear.cba.ufl.edu/cooke/MAR3503a/ttable.html presents the same information (for 90%, 95%, and 99%) in a slightly different way.

http://www.seismo.berkeley.edu/geology/labs/epma/student.htm presents the same information, but goes out to 50 df.

Hints and answers to HW 10

Due Assignment
20 March
  1. Read chapter 2 of the text, through page 26.
  2. Read chapter 6, pp 295-303, 305-309, 315-322, 324-345, 348-353, 360-361.
  3. Soil samples are obtained at "background" locations using a random sampling method.  The observed concentrations of nickel are 1, 1, 1, 5, and 80 ppm.  Estimate the background mean, standard deviation, variance, and 75th percentile:
  1. Using method of moments for a Normal distribution.
  2. Using method of moments for a Lognormal distribution.
  3. Using MLE for a Normal distribution.
  4. Using MLE for a Lognormal distribution.
  5. Using the MVUEs for a Normal distribution.
  6. * Using the MVUEs for a Lognormal distribution (use the spreadsheet on the How To... page).
  1. Groundwater samples are obtained at widely-spaced monitoring wells and measured for benzene.  Assume the concentrations act as if they are independent random samples of the groundwater being monitored.  The concentrations are 5, 6, 8, 13, and 215 micrograms per Liter (ppb).  Repeat questions (a) through (f) of the preceding problem.
  2. Find a table of Student's t.  (See, for example, the web pages listed above.)  Use it to figure out how to use Excel's TInv() function correctly.
  3. In problem 3, compute
  1. An upper 95% confidence limit (CL) of the mean, assuming a Normal distribution.  
  2. A lower 95% CL of the mean, assuming a Normal distribution.
  3. A two-sided 95% confidence interval (CI) for the mean, assuming a Normal distribution.
  4. An upper 95% CL for the mean, assuming a Lognormal distribution, using Land's method.  The H-factors are tabulated in a spreadsheet available on the How To... page.
  5. A lower 95% CL for the mean, assuming a Lognormal distribution, using Land's method.
  6. A two-sided 90% CI for the mean, assuming a Lognormal distribution.
  1. Same as problem 6, using the data in problem 4.
  2. An investigator obtains 40 samples of surface soil at a former transformer repair plant and claims the sample locations were chosen randomly.  Five of the analyses show PCBs in the samples.
  1. Compute upper CIs for the proportion of site surface soils containing PCBs having 80%, 90%, and 99% coverage.  Use the Normal approximation to the Binomial distribution.
  2. Compute lower CIs with 80%, 90%, and 99% confidence.
  3. Compute the answers to (a) and (b) exactly using the F-distribution formulas (5.95 and 5.96) in the text.  Use the binomial confidence limit spreadsheet available on the How To... page or refer to the Hahn & Meeker book (available at the library).  Identify any substantial differences in the answers and explain why they occur.
  1. Same as problem 8, assuming only one analysis exhibited any PCBs.

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This page was created 16 March and last updated 17 March (minor edits).