THIS IS ALL RELEVENT INFORMATION NEEDED FOR QUESTIONS ATTACHED:

A sports drink manufacturer is trying to appeal to a new niche market and creates three new flavours: "goji berry & chia" (GC), "lime & flax-seed" (LF) and "kale & spinach" (KS). They wish to market only the most popular of the three. To decide which is the most popular, randomly selected shoppers were given a free sample of one of the drinks. They were then asked to rate (out of 100) the drink they had (each shopper is only allowed to have one of the drinks).

A statistician was asked to analyse the data using ANOVA methodology, some of which is presented below. Unfortunately she was not able to complete the analysis and you have been asked to answer the questions below, which primarily concern finding the most popular out of the 3 suppliers.

AnovaModel.1 <- aov(rate ~ flavour, data = drinks)

summary(AnovaModel.1)

Df Sum Sq Mean Sq F value Pr(>F)

flavour 2 3420 1710 34.2 4.36e-12 *

Residuals 102 5100 50

Signif. codes: 0 '*' 0.001 '*' 0.01 '' 0.05 '.' 0.1 ' ' 1

with(courier, numSummary(time, groups = company, statistics = c("mean", "sd")))

mean var n

GC 34.93 49.446 35

KS 36.96 41.977 35

LF 23.97 58.564 35

Multiple Comparisons of Means: Tukey Contrasts

Fit: aov(formula = rate ~ flavour, data = drinks)

Linear Hypotheses:

Estimate Std. Error t value Pr(>|t|)

KS - GC==0 2.02 1.690 1.197 0.458

LF - GC==0 -10.97 1.690 -6.489 <0.00001 *

LF - KS==0 -12.99 1.690 -7.686 <0.00001 *

---

Signif. codes: 0 '*' 0.001 '*' 0.01 '' 0.05 '.' 0.1 ' ' 1

(Adjusted p values reported -- single-step method)

GC KS LF

"b" "b" "a"

leveneTest(score ~ make, data = cars, center = "median")

Levene's Test for Homogeneity of Variance (center = "median")

Df F value Pr(>F)

group 2 0.709 0.4945

102

unless otherwise indicated all questions in this test are talking about the ANOVA output above

The Questions below:

Question 1: Define relevent mean parameters and state the appropriate null and alternative hypothesis to be tested

Question 2: What is the value for the sum of squares with in?

Question 3: Under H0 what distribution does the test statistics follow?

Answers to the following is appreciated- time pressured :)