Quantitative methods Question 2022

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Quantitative Methods
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Quantitative Methods
Question 1
a. Column Scatter Plot
The green lines shown the variation within the groups.
The blue lines show the variation between the groups
The orange line shows the group mean
The short black lines show the individual means of each group.
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b. Test for Independence
The data to be used is shown in the table below.
Estate Southern Ridge Wine Valley Maisie and Co Kate's Corner
11.31 11.15 10.63 11.78 11.58
11.98 12.80 11.62 12.98 12.47
11.89 12.25 11.66 11.90 12.51
12.39 11.81 11.03 12.48 11.47
12.34 12.03 12.67 13.36 12.72
13.02 12.35 12.70 12.47 12.01
12.61 12.59 13.31 12.82 12.71
11.69 12.89 12.76 12.41 12.03
12.59 12.23 11.64 13.04 12.80
11.54 12.52 12.36 12.39 12.09
12.38 12.13 12.25 12.68 12.46
11.43 11.09 10.64 11.96 11.62
12.13 12.26 11.86 14.16 12.02
∑x 157.3 158.1 155.13 164.43 158.49
∑x^2 1906.51 1926.36 1859.62 2084.84 1934.73
Average 12.10 12.16 11.93 12.65 12.19
SS 3.18 3.62 8.44 5.06 2.49
The null and the alternative hypothesis are stated as:
Null hypothesis Ho : μ1=μ2=μ3=μ4 =μ5
Alternative hypothesis Hi :μ1 ≠ μ2 ≠ μ3 ≠ μ4=μ5
The assumption made is that each of the variables has the same variance.
The sample size n=13 while the number of groups a=5
The degrees of freedom:
df t =df B +df w
Degrees of freedom between groups:
df B=Ngroups−1
df B=5−1=4
The degrees of freedom between groups:
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