\" Respond to each of the following questions using this partially completed one

Question

" Respond to each of the following questions using this partially completed one-way ANOVA table:

"a. How many different populations are being considered in this analysis?

b. Fill in the ANOVA table with the missing values.

c. State the appropriate null and alternative

d. Based on the analysis of variance F-test, what conclusion should be reached regarding the null hypothesis? Test using a significance level of 0.01."

Please explain answers without using a graphing calculator or Excel spreadsheet. Thanks.

Source of Variation SSdf MS F-ratio 1,745 Between Samples Within Samples Total 240 6,504 246

Explanation / Answer

Using the equations to fill this table (regarding totals), consider:

a)

As df1 = 6, then

k = df1 + 1 = 7 populations [ANSWER]

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b)

See table above.

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c)

Ho: All the population means of the 7 groups we have are the same.

Ha: Not all the population means of the 7 groups we have are the same.

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d)

As for df1 = 6, df2 = 240, at 0.01 level,

Fcrit = 2.878

As F = 14.67 > 2.878, then we reject Ho.

There is significant evidence at 0.01 level that not all of the 7 means are equal. [CONCLUSION]

SV SS df MS F B 1745 6 290.8333 14.66695 W 4759 240 19.82917 T 6504 246

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