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The following is sample information. Test the hypothesis that the treatment mean

ID: 1092645 • Letter: T

Question

The following is sample information. Test the hypothesis that the treatment means are equal. Use the 0.05 significance level.

Treatment 1

Treatment 2

Treatment 3

5          

5          

6          

5          

4          

6          

8          

6          

6          

9          

3          

5          

(b)

What is the decision rule? (Round your answer to 2 decimal places.)

   Reject H0 if the test statistic is greater than .

(c&d)

Compute SST, SSE, and SS total and complete an ANOVA table. (Round SS, MS and F values to 3 decimal places.)

  Source

SS

df

MS

F

  Treatments

    

  

  

  

  Error

  

  

  

  Total

  

  

The following is sample information. Test the hypothesis that the treatment means are equal. Use the 0.05 significance level.

Explanation / Answer

the difference d between the mean of one population ?1 and the mean of another population ?2. (In the table, the symbol ? means " not equal to ".)

The first set of hypotheses (Set 1) is an example of a two-tailed test, since an extreme value on either side of the sampling distribution would cause a researcher to reject the null hypothesis. The other two sets of hypotheses (Sets 2 and 3) are one-tailed tests, since an extreme value on only one side of the sampling distribution would cause a researcher to reject the null hypothesis.

When the null hypothesis states that there is no difference between the two population means (i.e., d = 0), the null and alternative hypothesis are often stated in the following form.

H0: ?1 = ?2
Ha: ?1 ? ?2SE = sqrt[(s12/n1) + (s22/n2)]
SE = sqrt[(102/30) + (152/25] = sqrt(3.33 + 9) = sqrt(12.33) = 3.51

DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] }
DF = (102/30 + 152/25)2 / { [ (102 / 30)2 / (29) ] + [ (152 / 25)2 / (24) ] }
DF = (3.33 + 9)2 / { [ (3.33)2 / (29) ] + [ (9)2 / (24) ] } = 152.03 / (0.382 + 3.375) = 152.03/3.757 = 40.47

t = [ (x1 - x2) - d ] / SE = [ (78 - 85) - 0 ] / 3.51 = -7/3.51 = -1.99

Set Null hypothesis Alternative hypothesis Number of tails 1 ?1 - ?2 = d ?1 - ?2 ? d 2 2 ?1 - ?2> d ?1 - ?2 < d 1 3 ?1 - ?2< d ?1 - ?2 > d 1