Question

7. A consumer psychologist wishes to determine whether playing music increases sales at a local department store. To this end, the psychologist has the owner play either no music, soft rock, or classical music and notes the sales for 21 people (7 in each) under these three conditions. The dependent variable is dollars spent per shopper. The table below contains the data from this experiment. Perform a one-way ANOVA to address the consumer psychologist’s research question.

No Music	Soft Rock	Classical
119	68	85
123	31	67
157	88	55
198	59	99
188	67	63
146	71	58
173	87	51

Calculate the group means and grand mean and put your answers in the spaces provided.

No Music_____ Soft Rock_____ Classical_____

Grand Mean_____

8. Please write the null hypothesis for this analysis in both equation and written form.

9. Please write the research hypothesis for this analysis in both equation and written form.

10. Fill in the source table below based on your calculations.

Source	SS	df	MS	F
Between-Groups
Within-Groups
Total

11. Researchers were interested in how age is related to alcohol consumption. As such, they conducted a study dividing 150 subjects into 5 age groups and looking for average differences in alcohol consumption measured as drinking days per month. Sum of squares total is 1341. The authors of the study reported effect size eta-squared of .51. Find the value of the F-ratio.

Answer 1

(7) Means = Sum of Observations / Total Observations

No Music = 1104 / 7 = 157.71

Soft Rock = 471 / 7 = 67.29

Classical = 478 / 7 = 68.29

Overall Mean = Average of All Means = (157.71 + 67.29 + 68.29) / 3 = 97.76

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(8) The Null Hypothesis: H0: = = : The mean sales is the same for the different types of music.

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(9) The Research Hypothesis: Ha: : The mean of sales of at least 1 music is different from the others.

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(10) The ANOVA Table : Calculations are given at the end

Source	SS	DF	Mean Square	F
Between	37743.04	2	18871.52	35.14
Within/Error	9666.75	18	537.04
Total	47409.79	20

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(11) Eta Squared = SS between / SS Total

Therefore 0.51 = SS Between / 1341

SS between = 1341 * 0.51 = 683.91

Therefore SS Within = SS total - SS between = 1341 - 683.91 = 657.09

df between = k - 1 = 5 - 1 = 4

df within = N - k = 150 - 5 = 145

MS between = SS Between / df between = 683.91 / 4 = 170.98

MS within = SS within / df within = 657.09 / 145 = 4.53

F = MS between / MS within = 170.98 / 4.53 = 37.74

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Calculations for the ANOVA table in (10)

From the given data, we have

	No Music	Soft Rock	Classical
Total	1104	471	478
n	7	7	7
Mean	157.71	67.29	68.29
Sum Of Squares	5615.7207	2217.4287	1833.4287

Overall Mean as calculated is 97.76

SS treatment = SUM [n* ( - overall mean)²] = 7 * (157.71 - 97.76)² + 7 * (67.29 - 97.76)² + 7 * (68.29 - 97.76)² = 37743.04

df1 = k - 1 = 3 - 1 = 2

MSTR = SS treatment/df1 = 37743.04 / 2 = 18871.52

SSerror = SUM (Sum of Squares) = 5615.7207 + 2217.4287 + 1833.4287 = 9666.75

df2 = N - k = 21 - 3 = 18

Therefore MS error = SSerror/df2 = 9666.75 / 18 = 537.04

F = MSTR/MSE = 18871.52 / 537.04 = 35.14

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