Spring 2006
STAT 513 - Theory of Statistical Inference
Tuesday/Thursday 9:30-10:45
201A LeConte

Course Website: http://www.stat.sc.edu/~habing/courses/513F08.html

Extra Hmwk 2Due: Saturday, December 6th by 5:00pm Let T follow an exponential distribution with mean=5. Find the pdf, CDF, survivor function, hazard function, and cumulative hazard function.
Assignment 9Due: Thursday, December 4th 16.18 (instead of the applet you may use qgamma in R) and 16.24
Assignment 8Due: Tuesday, November 25th [in 7th] 16.10 a-e
Assignment 7Due: Thursday, November 13th [in 6th] 11.31, *, 11.47
[in 7th] 11.35, 11.52, 11.55

* 11.52 from 7th is not in 6th, the question is:
Is the plant density of a species related to the altitude at which data are collected? Let Y denote the species density and X denote the altitude. A fit of a simple linear regression model using 14 observatins yielded y-hat = 21.6 - 7.79x and r-squared=0.61.
a) What is the value of the correlation coefficient r?
b) What proportion of the variation in the densities is explained by the linear model using altitude as the independent variable?
c) Is there sufficient evidence at the alpha=0.05 to indicate that plant densities decrease with an increase in altitude?

Assignment 6Due: Tuesday, October 28th [in 6th] 11.6, 11.16, 11.4, 11.14a, 11.29 - For the last three do it both by hand, and using the computer package of your choice.
[in 7th] 11.10, 11.20, 11.8, 11.18a, 11.33 - For the last three do it both by hand, and using the computer package of your choice.
Assignment 5Due: Thursday, October 16th 10.105 [in 7th]/10.93 [in 6th]
Extra HmwkDue: Tuesday, October 7th
  • Use the modified Levene's test to test the hypothesis that the variance of nitrogen densities produced from chemical compounds is equal to the variance of of nigrogen densities produce from the atmosphere (using the data in 10.117 [in 7th]/10.103 [in 6th]). Report the p-value and your conclusion.
  • Assignment 4Due: Thursday, October 2nd
  • 10.99-10.100 (in 7th edition) / 10.87-10.88 (in 6th edition)
  • Assignment 3Due: Tuesday, Septbember 16th
  • 10.46 in 7th (10.36 in 6th)
  • 10.70a in 7th (10.58 in 6th) and find the p-value using R
  • 10.82a in 7th (10.70a in 6th) using the F test (Note that you need the raw data to do the modified Levene test, and so can't for this problem!)
  • 10.88 in 7th (10.76 in 6th) by hand -or- using R
  • Assignment 2Due: Tuesday, September 9th
  • Consider finding the power for a chi-squared test for a variance. Using the results of section 4.5 and the method of MGFs in 6.5 (both in 7th edition - the sections on the Gamma distribution and MGFs), what distribution does (n-1)s^2/sigma0^2 have when the Xi are IID normal with mean 0 and variance sigmaA^2? Use this result to find the power for testing sigma=40 versus sigma>40 when sigma is actually 45 (n=40, alpha=0.05). [Note that pgamma and qgamma are the cdf and inverse cdf functions for the gamma distribution in R].
  • Conduct a simulation study examining how robust the one-sample t-test is for t-distributions with df=5, 10, and 20, and for chi-squared distributions with df=5, 10, and 20. (Remember to use the right mu0 for the chi-squared ones!) What do you conclude about how the t-test is affected by heavy-tails and skewness?
  • Assignment 1Due: Tuesday, September 2nd
  • 10.2
  • Briefly state why you probably wouldn't actually want to use the methods of Section 10.3 in practice.
  • 10.78 in 7th Ed (10.66 in 6th Ed) - also calculate the p-values for parts b & c, and state what assumptions you needed to make.
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