Statistics 2MB3 - Assignment #3

2005-03-13 - Revised 2005-04-05

Due: 2005-04-06 18:00

Numbered exercises are from Devore, J.L. (2004) Probability and Statistics for Engineering and the Sciences, Sixth Edition, Brooks/Cole. Whenever possible, or unless instructed otherwise, do the calculations on your calculator, then again in R to check your results. You may submit either your calculator results or your R results.

Chapters 8

#62, #76

Chapter 8 - testing a variance

Consider a two-sided equal-tail test for the variance of a normal population. Derive the Operating Characteristic curve in terms of q = s2 / s02. Show that it can be computed by the following R code:

function (theta, n, alpha = 0.05) 
{
    pchisq(qchisq(1 - alpha/2, n - 1)/theta, n - 1) - pchisq(qchisq(alpha/2, 
        n - 1)/theta, n - 1)
}
Plot this curve for a = 0.05 and n = 2, 3, 5, 10, with all four curves on the same graph. Add a horizontal line through 0.95. Show that the test is "biased" in that there are some H1 values of s2 that are more likely to be accepted than the H0 value, but the bias becomes smaller as the sample size increases.

Chapter 9

For each exercise, give an appropriate graph and state your assumptions and conclusions.

#44, #62, #68, #72

Chapter 10

For each exercise, give an appropriate graph and state your assumptions and conclusions. Each time you do an ANOVA, give a 95% confidence interval for the residual variance.

#6, #26 (In (b) you only need to give m1-m2 and m1-m3, I don't expect all 15 comparisons.)

Chapter 11

For each exercise, give an appropriate graph and state your assumptions and conclusions. Each time you do an ANOVA, give a 95% confidence interval for the residual variance.

#22 (see Assignment #1 for a graph)

Chapter 12

For each exercise, give appropriate graphs and state your assumptions and conclusions. Each time you do an ANOVA, give a 95% confidence interval for the residual variance.

#19 (also give an ANOVA table with a test for non-linearity), #20 (also reproduce the MINITAB output in R and on your calculator)

Chapter 13

For each exercise, give appropriate graphs and state your assumptions and conclusions. Each time you do an ANOVA, give a 95% confidence interval for the residual variance.

#44 (Omit (e) and (f); see Assignment #1 for graphs; do the calculations in R)

In R, make a data frame flour with columns protein, starch, absorp. The following R code will give you everything you need to answer the questions. Note that you could also write absorp ~ starch + protein but it will give a slightly different ANOVA than absorp ~ protein + starch; why? In this example, you get the same conclusions either way so it doesn't matter which you do.

pairs(flour)
fitflour <- lm(absorp ~ protein + starch, data = flour)
anova(fitflour)
summary(fitflour)
plot(fitflour)
Statistics 2MB3

Last modified Tuesday, April 5, 2005 at 14:32