Question

Given the following sample information, test the hypothesis that the treatment means are equal at the 0.05 significance level.

Treatment 1	Treatment 2	Treatment 3
3	9	6
2	6	3
5	5	5
1	6	5
3	8	5
1	5	4
	4	1
	7	4
	6
	4

(a) State the null hypothesis and the alternate hypothesis. Ho : ?1 (>, <, or =) incorrect ?2 = (<,>, or =) ?3. H1 : Treatment means are not ___ all the same

(b) What is the decision rule?(Round your answer to 2 decimal places.) Reject Ho if F >

(c) Compute SST, SSE, and SS total. (Round your answers to 2 decimal places.)

SST = SSE = SS total =

(d) Complete the ANOVA table. (Round SS, MS and F values to 2 decimal places.)

Source SS df MS F Treatments

(e) State your decision regarding the null hypothesis.

(f) Find the 95% confidence interval for the difference between treatment 2 and 3. (Round your answers to 2 decimal places.) 95% confidence interval is: n/r incorrect ± n/r incorrect We can conclude that the treatments 2 and 3 are ?

Answer 1

the null hypothesis and the alternate hypothesis is

H₁ : Treatment means are not equal for at least one treatment

(b) The decision rule is reject null hypothesis when F>F_tabulated

i.e.p-value is less than level of significance.

(c), (d)

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Column 1	6	15	2.5	2.3
Column 2	10	60	6	2.666667
Column 3	8	33	4.125	2.410714
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	47.625	2	23.8125	9.547733	0.001124	3.4668
Within Groups	52.375	21	2.494048
Total	100	23

(e) We reject the null hypothesis and concluded that the treatment meanss are different.

(f) 95% confidence interval for the difference between treatment 2 and 3