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The marketing department of a company has designed three different boxes for its product. It wants to determine which box will produce the largest amount of sales. Each box will be test marketed in five different stores for a period of a month. Information on sales is provided below.

	Store 1	Store 2	Store 3	Store 4	Store 5
Box 1	210	230	190	180	190
Box 2	195	170	200	190	193
Box 3	295	275	290	275	265

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What are the null and alternative hypotheses in this case?

Select one:

a. H_o: μ ₁ = μ ₂                                        H_a: μ ₁ = μ ₃

b. H_o: μ ₁ = μ 3                                       H_a: μ ₃ = μ ₂

c. H_o: μ ₁ = μ ₂ = μ 3                               H_a: all means are different

d. H_o: μ ₁ = μ ₂ = μ 3                               H_a: at least one mean is different

e. H_o: μ₁ = μ₂                                          H_a: μ₂ = μ₃

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The treatments sum of squares is

Select one:

a. 27,400.41

b. 711.07

c. 2,022.14

d. 2,466.72

e. 24,467.2

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The error sum of squares is

Select one:

a. 27,400.41

b. 2,022.14

c. 24,667.2

d. 2,466.72

e. 711.07

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The blocks degrees of freedom are

Select one:

a. 8

b. 14

c. 6

d. 4

e. 2

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The total degrees of freedom are

Select one:

a. 6

b. 2

c. 4

d. 14

e. 8

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The treatments mean square is

Select one:

a. 12,233.60

b. 6,166.80

c. 1,233.36

d. 177.77

e. 252.77

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The F statistic is

Select one:

a. 48.4

b. 24.7

c. 69.38

d. 8.65

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With α = 0.01, critical F statistic is

Select one:

a. 4.46

b. 6.06

c. 8.65

d. 46.4

e. 48.4

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What conclusion do you draw?

Select one:

a. Do not reject H_o: all means are equal.

b. Do not reject H_o: all means are different.

c. Reject H_o: at least one mean is different from others.

d. The test result is inconclusive.

e. Reject H_o: all means are equal.

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With α = 0.01, the value of Fisher’s LSD is

Select one:

a. 28.37

b. 31.87

c. 32.68

d. 33.73

e. 29.12

Question 23

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Based on the LSD test above, which (if any) is different from the others?

Select one:

a. The mean of box 1 is different from the others.

b. All means are different.

c. All means are equal.

d. The mean of box 2 is different from the others.

e. The mean of box 3 is different from the others

Answer 1

using excel data analysis tool for two factor anova, following o/p Is obtained : write data>menu>data>data analysis>anova :two factor without replication>enter required labels>ok, and following o/p Is obtained,

Anova: Two-Factor Without Replication
SUMMARY	Count	Sum	Average	Variance
1	3	700	233	2908.333
2	3	675	225	2775.000
3	3	680	227	3033.333
4	3	645	215	2725.000
5	3	648	216	1803.000
Box 1	5	1000	200	400.000
Box 2	5	948	142	133.300
Box 3	5	1400	134	150.000
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Rows	711.07	4	177.77	0.703	0.6114	7.01
Columns	24467.20	2	12233.60	48.399	0.0000	8.65
Error	2022.13	8	252.77
Total	27200.40	14

13)  

d. H_o: μ ₁ = μ ₂ = μ 3                               H_a: at least one mean is different

14) 24467.20  

15) 2022.13  

16) 4

17) 14

18)  12,233.60

19) 48.4

20) c. 8.65

21) c. Reject Ho: at least one mean is different from others.

22)

Fishers LSD critical value=tα/2,df √(MSE(1/ni+1/nj)) = 33.73

23)

if absolute difference of means > critical value,means are significnantly different ,otherwise not                      
                      

population mean difference		critical value			result
µ1-µ2	10.400	33.73			means are not different
µ1-µ3	80.000	33.73			means are different
µ2-µ3	90.400	33.73			means are different

e. The mean of box 3 is different from the others