Question

The following data are given for a two-factor ANOVA with two treatments and three blocks.

  

	Treatment
Block	1	2
A	46	31
B	37	26
C	44	35

  

Using the 0.05 significance level conduct a test of hypothesis to determine whether the block or the treatment means differ.

   

a.	State the null and alternate hypotheses for treatments.

H0	(Click to select)The means are the same.The standard deviations are the same.The standard deviations are different.The means are different.
H1	(Click to select)The means are the same.The standard deviations are the same.The standard deviations are different.The means are different.

  

b.	State the decision rule for treatments. (Round your answer to 1 decimal place.)

  (Click to select)RejectDo not reject H₀ if the test statistic is greater than .

  

c.	State the null and alternate hypotheses for blocks. (Round your answer to 1 decimal place.)

H0	(Click to select)The means are the same.The standard deviations are the same.The standard deviations are different.Atleast one mean is different.
H1	(Click to select)The standard deviations are the same.At least one mean is different.The standard deviations are different.The means are the same.

  

Also, state the decision rule for blocks.

(Click to select)RejectDo not reject H₀ if the test statistic is greater than .

d. & e.	Compute SST, SSB, SS total, and SSE and complete an ANOVA table. (Round SS, MS values to 3 decimal places, F value to 2 decimal places and Total to 4 decimal places.)

Source	SS	df	MS	F
Treatments
Blocks
Error
Total

  

f.	Give your decision regarding the two sets of hypotheses.

  Decision: Treatments. (Click to select)RejectDo not reject H₀

  Decision: Blocks. (Click to select)RejectDo not reject H₀

Answer 1

Ho:The means are the same.

Ha: .The means are different.

b)

decision rule :reject Ho if test statsitic F >18.5

c)

Ho:The means are the same.

Ha: .The means are different.

d)decision rule :reject Ho if test statsitic F >19

d)

Source of Variation	SS	df	MS	F
treatment	204.167	1	204.167	43.75
block	76.000	2	38.000	8.14
Error	9.333	2	4.667
Total	289.500	5

f)

  Decision: Treatments :reject Ho

Decision: Blocks. : Do not reject ho