Question

Use the following scenario and data to answer questions 12.1 – 12.5. A researcher is interested in how many days it takes athletes to recover from jet lag when they have had to fly a long distance. It is commonly known that traveling east (moving “ahead” in time) leads to more serious jet lag than travelling west. The researcher finds 18 professional athletes who just travelled a long distance; six stayed in the same time zone, six travelled west, and six travelled east.

Traveling West	Traveling East	Travel in Same Time Zone
3	5	1
3	3	2
2	6	1
3	7	1
2	4	0
2	8	1
M = 2.5	M = 5.5	M = 1
SS =	SS =	SS =

12.1 Calculate the sum of squares for each treatment condition (SHOW WORK)

SS_w =                                         SS_e =                                          SS_s =

12.2 What is the value of N in this experiment?

12.3 What number should appear in the denominator of your F-ratio? (I want the actual number, not the name of it)

12.4 What number should appear in the numerator of your F-ratio? (I want the actual number, not the name of it) (SHOW WORK)

12.5 Do the data show a significant difference in jet lag depending on the direction of travel? Use a two-tailed test and alpha = .05.

Answer 1

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(12.1) Sum of squares = SUM [(X - Mean)²]

SSw = (3 - 2.5)² + (3 - 2.5)² + (2 - 2.5)² + (3 - 2.5)² + (2 - 2.5)² + (2 - 2.5)² = 0.25 + 0.25 + 0.25 + 0.25 + 0.25 + 0.25 = 1.5

SSe = (5 - 5.5)² + (3 - 5.5)² + (6 - 5.5)² + (7 - 5.5)² + (4 - 5.5)² + (8 - 5.5)² = 0.25 + 6.25 + 0.25 + 2.25 + 2.25 + 6.25 = 17.5

SSs = (1 - 1)² + (2 - 1)² + (1 - 1)² + (1 - 1)² + (0 - 1)² + (1 - 1)² = 0 + 1 + 0 + 0 + 1 + 0 = 2

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(12.2) The number of columns, k = 3

Number of subjects in each column, n = 6

Therefore N = 6 * 3 = 18

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(12.3) SS error = SUM (Sum of squares) = 1.5 + 17.5 + 2 = 21

DF error = N - k = 18 - 3 = 15

Therefore the number in the denominator (MS error) = SS error / DF error = 21/15 = 1.4

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(12.4) SS treatment = SUM[ n * (Mean - GM)²]

GM = (2.5 + 5.5 + 1)/3 = 9 /3 = 3

SS treatment = 6 * (2.5 - 3)² + 6 * (5.5 - 3)² + 6 * (1 - 3)² = 6 * 0.25 + 6 * 6.25 + 6 * 4 = 1.5 + 37.5 + 24 = 63

DF treatment = k - 1 = 3 - 1 = 2

Therefore the number in the numerator of the F ratio (MS treatment) = 63/2 = 31.5

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(12.5)

The Hypothesis:

H0: The means of all the groups are equal.

Ha: There is a difference between the means of at least 2 of the groups.

The Test Statistic:

The ANOVA Table is as below

Source	SS	DF	Mean Square	F
Between	63.00	2	31.50	22.50
Within/Error	21.00	15	1.40
Total	84.00	17

F test = 22.5

The p value: (2 tailed) for Ftest = 22.5; P value = 0

The Decision Rule: By the p value method is that if p value is < , then reject H0.

The Decision: Since p value(0) is < (0.05), we reject H0.

The Conclusion: There is sufficient evidence at the 0.05 level to conclude that there is a difference in the means of at least 2 of the means.

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