R-CODE

The following data includes information on agricultural land sale in four major regions of Minnesota for the period 2002-2011. Below is a summary of the dataset

## Loading required package: car 

## Loading required package: effects 

## Loading required package: carData 

## ## Attaching package: 'carData' 

## The following objects are masked from 'package:car': ## ## Guyer, UN, Vocab 

## lattice theme set by effectsTheme() ## See ?effectsTheme for details. 

## acrePrice region ## Min. :4.956 A:4198 ## 1st Qu.:7.684 B:2583 ## Median :8.025 C:2832 ## Mean :8.008 D:1991 ## 3rd Qu.:8.385 

## Max. :9.616 

We want to test at the 5% significance level that H0 :?A =?B =?C =?D vs H? :atleasttwoofgroupmeansarenotequal

where ?A,?B,?C,?D are the mean of the land price in each region. Using R, an ANOVA table was computed as follows:

## ## region ## Residuals ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

(a) What would be the assumption that we should make before conducting this hypothesis test?

(b) Using the output above, report the observed test statistic. What is the distribution of the test statistic under H0? State the values for its parameters.

(c) Report the p-value for this test and state the conclusion.

(d) Tukey HSD is conducted to investigate the pairwise differences among the population means. Interpret the following output from R. Specifically, state the price between which pairs of regions are different and which are not different.

## Tukey multiple comparisons of means ## 95% family-wise confidence level ## ## Fit: aov(formula = acrePrice ~ region, data = Minndata) ## 

## $region ## diff lwr upr p adj ## B-A -0.018229502 -0.05261848 0.01615948 0.5233333 ## C-A 0.215393031 0.18195308 0.24883298 0.0000000 ## D-A 0.220616746 0.18319628 0.25803721 0.0000000 ## C-B 0.233622533 0.19620749 0.27103757 0.0000000 ## D-B 0.238846248 0.19783471 0.27985779 0.0000000 ## D-C 0.005223715 -0.03499537 0.04544280 0.9871941 

Hint for importing the data:

anorexia = read.table("http://users.stat.umn.edu/~guxxx192/courses/data/anorexia.txt",header = TRUE)

attach(anorexia)

Hint for (a): Use t.test command to find the confidence interval for population mean difference.

Hint for (b): Use TukeyHSD command to find the Tukey 95