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StatTutor Lesson - The Analysis of Variance F test

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      Question 1

      65

      Question 1.

      What is an equivalent way to restate the alternative hypothesis, "not all means are equal," for testing multiple means?

      A.
      B.
      C.

      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.
      2

      Question 2

      133

      Question 2.

      How many means need to be compared for this study?

      A.
      B.
      C.
      D.
      E.

      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.
      2

      Question 3

      156

      Question 3.

      What is the null hypothesis for this study?

      A.
      B.
      C.
      D.

      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.
      2

      Question 4

      227

      Question 4.

      On the basis of the boxplots, which color has the highest mean number of trapped beetles?

      A.
      B.
      C.
      D.
      E.

      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.
      2

      Question 5

      230

      Question 5.

      On the basis of the sample standard deviations, is the largest standard deviation more than twice as large as the smallest standard deviation?

      A.
      B.

      Incorrect. The largest standard deviation is 6.795 and the smallest standard deviation is 3.764. 6.7953.764 = 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. 6.7953.764 = 1.81, so the largest is not more than twice as large the smallest.
      Incorrect. Try again.
      2

      Question 6

      302

      Question 6.

      Why is the condition of Normality met?

      A.
      B.
      C.

      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.
      2

      Question 7

      322

      Question 7.

      At α = 0.05, can we reject the null hypothesis, H0: µ1 = µ2 = µ3 = µ4?

      A.
      B.

      Incorrect. Since P-value = 0.000 is less than α = 0.05, we can reject the null hypothesis.
      Correct. Since P-value = 0.000 is less than α = 0.05, we can reject the null hypothesis.
      Incorrect. Try again.
      2

      Question 8

      353

      Question 8.

      Two of the means for the four color do not differ significantly. On the basis of these boxplots, which means are these?

      A.
      B.
      C.
      D.
      E.
      F.

      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.
      2

      Questions 9-10

      383

      Question 9.

      Fill in the blank: The mean of the color ___________ is significantly higher than the other means.

      A.
      B.
      C.
      D.

      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.
      2

      Questions 11-12

      432

      Question 11.

      Which intervals do NOT overlap with any other interval?

      A.
      B.
      C.
      D.
      E.
      F.

      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.
      2

      Question 13

      528

      Question 13.

      According to the individual confidence intervals given in this output, can we say that the mean for "List 2" differs significantly from the means for the other lists?

      A.
      B.

      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.
      2