#62, #76
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.
For each exercise, give an appropriate graph and state your assumptions and conclusions.
#44, #62, #68, #72
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.)
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)
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)
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 columnsprotein
,starch
,absorp
. The following R code will give you everything you need to answer the questions. Note that you could also writeabsorp ~ starch + protein
but it will give a slightly different ANOVA thanabsorp ~ 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)
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