Chapter 1. The Analysis of Variance F test

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Stat Tutor
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1:05

Question 1.1

Incorrect. Saying "at least one mean is different" is equivalent to "not all means are equal." But saying "all means are different" is not equivalent and is incorrect, because one mean may be different, but the rest may be equal.
Correct. Saying "at least one mean is different" is equivalent to "not all means are equal." But saying "all means are different" is not equivalent and is incorrect, because one mean may be different, but the rest may be equal.
Incorrect. Try again.
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2:13

Question 1.2

Incorrect. Four colors are to be tested so we need to compare four means.
Correct. Four colors are to be tested so we need to compare four means.
Incorrect. Try again.
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2:36

Question 1.3

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Incorrect. We want to test whether four means are equal, so the null hypothesis is H0: µ1 = µ2 = µ3 = µ4 which includes symbols for four means.
Correct. We want to test whether four means are equal, so the null hypothesis is H0: µ1 = µ2 = µ3 = µ4 which includes symbols for four means.
Incorrect. Try again.
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3:47

Question 1.4

Incorrect. The boxplot for yellow is much higher than the boxplots for the other colors, so, it will have the largest mean.
Correct. The boxplot for yellow is much higher than the boxplots for the other colors, so, it will have the largest mean.
Incorrect. Try again.
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3:50

Question 1.5

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Incorrect. The largest standard deviation is 6.795 and the smallest standard deviation is 3.764. $$\frac{6.795}{3.764}$$ = 1.81, so the largest is not more than twice as large the smallest.
Correct. The largest standard deviation is 6.795 and the smallest standard deviation is 3.764. $$\frac{6.795}{3.764}$$ = 1.81, so the largest is not more than twice as large the smallest.
Incorrect. Try again.
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5:02

Question 1.6

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Incorrect. With total sample size = 6 + 6 + 6 + 6 = 24, the total sample size is not large enough to apply the Central Limit Theorem. (To apply the Central Limit theorem, the total sample size needs to be at least 40.) But there are no outliers displayed in the boxplots, so Normality is ok.
Correct. With total sample size = 6 + 6 + 6 + 6 = 24, the total sample size is not large enough to apply the Central Limit Theorem. (To apply the Central Limit theorem, the total sample size needs to be at least 40.) But there are no outliers displayed in the boxplots, so Normality is ok.
Incorrect. Try again.
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5:22

Question 1.7

Incorrect. Since P-value = 0.000 is less than $$\alpha$$ = 0.05, we can reject the null hypothesis.
Correct. Since P-value = 0.000 is less than $$\alpha$$ = 0.05, we can reject the null hypothesis.
Incorrect. Try again.
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5:53

Question 1.8

Incorrect. Because the boxplots for blue and white are at about the same height, their means do not differ significantly.
Correct. Because the boxplots for blue and white are at about the same height, their means do not differ significantly.
Incorrect. Try again.
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6:23

Question 1.9

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Incorrect. The boxplot for the color yellow is much higher than the other boxplots.
Correct. The boxplot for the color yellow is much higher than the other boxplots.
Incorrect. Try again.
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Question 1.10

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Incorrect. The yellow interval is the farthest to the right and gives the highest estimated mean.
Correct. The yellow interval is the farthest to the right and gives the highest estimated mean.
Incorrect. Try again.
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7:12

Question 1.11

p1BpUKi9zbXFKjJulU0Hl2GXSALoAmCNWaN/8TklJ29P+/zF4TYd9VSXfboXefb9tOX63z6ZWy6X2LSjgltRe5V3LkDh+SwqqbNPfBzUqa2so+tHBQ4sS7HTn+qcqOcE8rGbe5O8il9zl/ySG3GxoyTGHWhr2huy0DIQGDos9TMBQy+JYOcYQsmiPC/vUfSZbZpRN7fPXIDp/UjqSy7C5BwAX0XHTK7JudmpbLYLMvDmXf7vFVlvvG3eTBDaJH5kMQKsCOebdQno2DB8zusZIepse6dnmmvXQvIGUJqbWBi/9xSiKp/Ibt8Rj1ziMEe71KzdQUrM2MskXGPnj+4Pd9hC6G0=
Incorrect. the yellow and green intervals do not overlap with any other intervals.
Correct. the yellow and green intervals do not overlap with any other intervals.
Incorrect. Try again.
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Question 1.12

Incorrect. The interval for the color yellow has the highest estimated mean and it does not overlap with any other interval. So it is the recommended color.
Correct. The interval for the color yellow has the highest estimated mean and it does not overlap with any other interval. So it is the recommended color.
Incorrect. Try again.
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8:48

Question 1.13

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Incorrect. The confidence interval for "List 2" overlaps with all of the other intervals. Therefore, we cannot say that it differs significantly from any of the means for the other lists.
Correct. The confidence interval for "List 2" overlaps with all of the other intervals. Therefore, we cannot say that it differs significantly from any of the means for the other lists.
Incorrect. Try again.
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