(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
where are the mean values
is a critical value of the studentized range for α, the number of treatments or samples r, and the within-groups degrees of freedom . We get this value from studentized range table.
is the within groups mean square from the ANOVA table and n is the sample size for each treatment.
From Anova table,
= 742.33 , = 18
n = 10, r = 3
For 95% confidence interval , = 0.05
From studentized range table, = 3.61
So,
So,
Tukey simultaneous 95 percent confidence interval for
Coke Classic - New Coke = 100.2 - 65.2 31.103 = 35 31.103 = (35 - 31.103, 33.7 + 31.103) = (3.90, 64.80)
Coke Classic – Pepsi = 100.2 - 74.1 31.103 = 26.1 31.103 = (26.1 - 31.103, 26.1 + 31.103) = (-5.00, 57.20)
New Coke – Pepsi = 65.2 - 74.1 31.103 = -8.9 31.103 = (-8.9 - 31.103, -8.9 + 31.103) = (-40.00, 22.20)
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