Please show all of your work. Assume =0.05 for all questions regarding statistic

Question

Please show all of your work. Assume =0.05 for all questions regarding statistical significance.

1. A researcher is interested in the effects of music preference on alcohol consumption. He determines the weekly alcohol consumption of 4 groups of subjects: rock music fans, country music fans, hip-hop fans, and classical music fans. His data are reproduced below; each score represents weekly alcohol consumption (number of drinks) for each of his subjects.

Rock Music

Country Music

Hip-hop

Classical Music

9

14

3

1

2

6

10

3

5

11

9

2

4

12

4

0

7

9

2

5

7

7

5

1

8

8

6

6

Does music preference affect alcohol consumption? Be sure to show each step in your hypothesis testing approach and to include a completed ANOVA table (8 points).

Rock Music

Country Music

Hip-hop

Classical Music

9

14

3

1

2

6

10

3

5

11

9

2

4

12

4

0

7

9

2

5

7

7

5

1

8

8

6

6

Explanation / Answer

Step 1

null, Ho: µ1 =µ2 =µ3 =µ4

alternative, H1: one of the mean is diffrent to each other

Step 2

Degrees of freedom between = k - 1 = 4 - 1 = 3

Degrees of freedom Within = n - k = 28 - 4 = 24

Degrees of freedom Total F( k-1,n - k,) at 0.05 is = F Crit = 3.009

Step 3

Grand Mean = G / N = 6+9.571+5.571 +2.571 / 4 = 5.928

SST = ( Xi - GrandMean)^2 = (9-5.928)^2 + (2-5.928)^2 + (5-5.928)^2 + ……..& so on = 172.71

SS Within = (Xi - Mean of Xi ) ^2 =,(9-6)^2 + (2-6)^2 + (5-6)^2 + ……..& so on = 169.14

SS Between = SST - SS Within = 233.277 - 132.776 = 341.86

Step 4

Mean Square Between = SS Between / df Between = 57.571

Mean Square Within = SS Within / df Within = 7.048

Step 5

F Cal = MS Between / Ms Within = 8.17

We got |F cal| = 8.17 & |F Crit| =3.009

MAKE DECISION

Hence Value of |F cal| > |F Crit|and Here We Reject Ho

we claim that music preference affect alcohol consumption

Treatments ONE WAY ANOVA Mean = X /n Rock 9 2 5 4 7 7 8 6 Country 14 6 11 12 9 7 8 9.571 Hip Hop 3 10 9 4 2 5 6 5.571 Classical 1 3 2 0 5 1 6 2.571

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