Question

The Coca-Cola Company introduced New Coke in 1985. Within three months of this introduction, negative consumer reaction forced Coca-Cola to reintroduce the original formula of Coke as Coca-Cola Classic. Suppose that two years later, in 1987, a marketing research firm in Chicago compared the sales of Coca-Cola Classic, New Coke and Pepsi in public building vending machines. To do this, the marketing research firm randomly selected 10 public buildings in Chicago having both a Coke machine (selling Coke Classic and New Coke) and a Pepsi machine The Coca-Cola Data and a MINITAB Output of a Randomized Block ANOVA of the Data Building 151 15 2 Coke Classic New Coke Pepsi 40 72 45 30 97 108 3 54 47 72 131 136 64 213 151 105 56 90 147 64 40 10 Two-way ANOVA: Cans versus Drink, Building DF MS 8,618.1 Drink Building Error Total 3,309.03 52,684.2 5,853.80 742.33 4.46 7.89 18 13,361.9 72,664.2 29 Descriptive Statistics: Cans Variable Mean 100.2 Coke Classic New Coke Pepsi 74.1 (a-1) Calculate the value of the test statistic and p-value. (Round "test statistic" value to 2 decimal places and "p-value" to 3 decimal places.) Test statistic p-value 027 (a-2) At the 0.05 significance level, what is the conclusion? Reject Ho ODo not reject Ho (b) What is the Tukey simultaneous 95 percent confidence interval for the following? (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places. Confidence interval Coke Classic New Coke Coke Classic Pepsi New Coke - Pepsi

Answer 1

(a-1)

By given output,

F test statistic for comparing the differences between various drinks = 4.46

P-value for F = 4.46 is  0.027

a-2)

As, p-value is less than the 0.05 significance level, Reject H0

(b)

Tukey 95 percent confidence interval is calculated using the below formula

$x_i - x_j \pm q(\alpha, r, df_w) \sqrt{MS_w / n}$

where $x_i , x_j$ are the mean values

$q(\alpha, r, df_w)$ is a critical value of the studentized range for α, the number of treatments or samples r, and the within-groups degrees of freedom $df_w$. We get this value from studentized range table.

$MS_w$ is the within groups mean square from the ANOVA table and n is the sample size for each treatment.

From Anova table,

$MS_w$ = 742.33 , $df_w$ = 18

n = 10, r = 3

For 95% confidence interval , $\alpha$ = 0.05

From studentized range table, $q(0.05, 3, 18)$ = 3.61

So, $q(\alpha, r, df_w) \sqrt{MS_w / n} = 3.61 \sqrt{742.33 / 10} = 31.10325$

So,

Tukey simultaneous 95 percent confidence interval for

Coke Classic - New Coke = 100.2 - 65.2 $\pm$ 31.103 = 35 $\pm$ 31.103 = (35 - 31.103, 33.7 + 31.103) = (3.90, 64.80)

Coke Classic – Pepsi = 100.2 - 74.1 $\pm$ 31.103 = 26.1 $\pm$ 31.103 = (26.1 - 31.103, 26.1 + 31.103) = (-5.00, 57.20)

New Coke – Pepsi = 65.2 - 74.1 $\pm$ 31.103 = -8.9 $\pm$ 31.103 = (-8.9 - 31.103, -8.9 + 31.103) = (-40.00, 22.20)