Extra Hmwk 2 | Due: 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.
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Assignment 9 | Due: Thursday, December 4th |
16.18 (instead of the applet you may use qgamma in R) and 16.24
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Assignment 8 | Due: Tuesday, November 25th |
[in 7th] 16.10 a-e
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Assignment 7 | Due: 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?
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Assignment 6 | Due: 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.
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Assignment 5 | Due: Thursday, October 16th |
10.105 [in 7th]/10.93 [in 6th]
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Extra Hmwk | Due: 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.
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Assignment 4 | Due: Thursday, October 2nd |
10.99-10.100 (in 7th edition) / 10.87-10.88 (in 6th edition)
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Assignment 3 | Due: 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
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Assignment 2 | Due: 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?
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Assignment 1 | Due: 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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