A regional opera company has tried three different approaches to solicit donatio

Question

A regional opera company has tried three different approaches to solicit donations from 24 potential sponsors. The 24 potential sponsors were randomly divided into three groups of eight, and one approach was used for each group. The dollar amounts of the resulting contributions are shown in the table belpw Find the values of I,J,MSTr and MSE "by-hand". That is, provide formulas for all your computations and show results of any intermediate steps. Carefully formulate the null hypothesis and alternative for the ANOVA F-test in words in the context of this problem. Find the value of the F_test statistic "by-hand" and the associated p-value using a table, your calculator or a computer. Formulate a conclusion for the test.

Explanation / Answer

From Excel

a) SST=8157398

SSE=1232261

SSTr=1211074

SSb=5714063

b)

Null hyp: All the treatment means are equal

Alternative hyp: Atleast one treatment is not same

alpha:5% level

c)

Test statistic:

F cal=7.86

P value=0.0041

d)Conclusion: P=0.0041 <0.05 we reject te null hypothesis. Hence results are significant

Anova: Two-Factor Without Replication SUMMARY Count Sum Average Variance Row 1 9 10451 1161.222 265820.9 Row 2 9 13902 1544.667 399506 Row 3 9 9453 1050.333 202963.5 Column 1 3 6 2 1 Column 2 3 3400 1133.333 103333.3 Column 3 3 4300 1433.333 163333.3 Column 4 3 4400 1466.667 213333.3 Column 5 3 4500 1500 90000 Column 6 3 4800 1600 160000 Column 7 3 4350 1450 97500 Column 8 3 3800 1266.667 213333.3 Column 9 3 4250 1416.667 180833.3 ANOVA Source of Variation SS df MS F P-value F crit Rows 1211074 2 605537.1 7.862453 0.004186 3.633723 Columns 5714063 8 714257.8 9.274111 9.68E-05 2.591096 Error 1232261 16 77016.31 Total 8157398 26

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