Answer:
Blue
Step-by-step explanation:
Given
[tex]Red = 10[/tex]
[tex]Blue = 10[/tex]
[tex]Green = 10[/tex]
[tex]Yellow = 10[/tex]
[tex]Total = 10 + 10 + 10 + 10 = 40[/tex]
[tex]trials = 7[/tex]
See attachment for complete question
From the attached figure;
The observed frequency of each is:
[tex]Red = 1[/tex]
[tex]Blue = 2[/tex]
[tex]Green = 0[/tex]
[tex]Yellow = 4[/tex]
Next is to calculate the probability of each of the colors.
[tex]P(Red) = \frac{Red}{Total} = \frac{10}{10 + 10 +10 +10} =\frac{10}{40} = \frac{1}{4}[/tex]
[tex]P(Blue) = \frac{Blue}{Total} = \frac{10}{10 + 10 +10 +10} =\frac{10}{40} = \frac{1}{4}[/tex]
[tex]P(Green) = \frac{Green}{Total} = \frac{10}{10 + 10 +10 +10} =\frac{10}{40} = \frac{1}{4}[/tex]
[tex]P(Yellow) = \frac{Yellow}{Total} = \frac{10}{10 + 10 +10 +10} =\frac{10}{40} = \frac{1}{4}[/tex]
The expected frequency of each is:
[tex]Expected = Probability * trials[/tex]
So:
[tex]Red = \frac{1}{4} * 7 = 1.75[/tex]
[tex]Blue = \frac{1}{4} * 7 = 1.75[/tex]
[tex]Green= \frac{1}{4} * 7 = 1.75[/tex]
[tex]Yellow= \frac{1}{4} * 7 = 1.75[/tex]
By comparison the expected frequencies with the observed frequencies;
The closest is Blue.
Observed frequency Expected Absolute difference
[tex]Red = 1[/tex] [tex]1.75[/tex] [tex]|1-1.75| = 0.75[/tex]
[tex]Blue = 2[/tex] [tex]1.75[/tex] [tex]|2-1.75| = 0.25[/tex]
[tex]Green = 0[/tex] [tex]1.75[/tex] [tex]|0-1.75| = 1.75[/tex]
[tex]Yellow = 4[/tex] [tex]1.75[/tex] [tex]|4-1.75| = 1225[/tex]
This is so because; blue has the least absolute difference.
