Question

Given the following sample information, test the hypothesis that the treatment means are equal at the 0.10 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	5
	6
	4

a. State the null hypothesis and the alternative hypothesis.

H₀ : μ₁ =  Correctμ₂   =  Correctμ₃

H₁ : Treatment means are not  Correct all the same.

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

Reject H₀ if F >                2.58 2.58 Incorrect .

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

SST =                46.96 46.96 Incorrect

SSE =                53 53 Incorrect

SS total =                99.96 99.96 Incorrect  

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

	Source	SS	DF	MS	F
	Factor	46.96 46.96 Incorrect	2 2 Correct	23.48 23.48 Incorrect	9.30 9.30 Incorrect
	Error	53 53 Incorrect	21 21 Correct	2.53 2.53 Incorrect
	Total	99.96 99.96 Incorrect	23 23 Correct

e. State your decision regarding the null hypothesis.

Decision: Reject  CorrectH_0.

f.Find the 95% confidence interval for the difference between treatment 2 and 3. (Round the final answers to 2 decimal places.)

95% confidence interval is: 0.13 0.13 Incorrect   ±   3.37 3.37 Incorrect  

We can conclude that the treatments 2 and 3 are different  Correct .

Answer 1

GIVEN a sample information in the way of three treatments and asked to solve the following

now

TO FIND:-a)State the null hypothesis and the alternative hypothesis.

SO we have that now

H0:

@- Treatments means all the same

H1:

@-Treatments means all not the same.

TO FIND:-b)What is the decision rule?

NOW we actualy we know that we have,

=0.10

Degrees of Freedom for numerator = 3 - 1 = 2

Degrees of Freedom for denominator = 24 - 3 = 21

now

taking the critical value of F = 2.575 (since from the table)

so the answer is :-

Decision Rule:
Reject H0 if F > 2.575

TO FIND :-c)Compute SST, SSE, and SS total.

So we can compute only through the table

Fromthe given data, the following Table is calculated:

	Treatment 1	Treatment 2	Treatment 3
n	6	10	8
Sum	15	60	34
Mean	2.5	6.0	4.25
	49	384	162
Std. Dev.	1.517	1.633	1.581
SS	11.5	24.0	17.5

*for finding theSSTwe have a formula = sstotal-sse:-

** now finding SSE:-

*** now finding SS TOTAL:-

THERE FORE SS TOTAL -

TO FIND :-d)Complete the ANOVA table?

The ANOVA Table is completed as follows:

Source	SS	DF	MS	F
Factor	46.958	2	46.958/2=23.479	23.479/2.528=9.303
Error	53.0	21	53.0/21=2.528
Total	99.958	23

Now using the data i have completed the ANOVA table above

TO FIND:-e)State your decision regarding the null hypothesis.

Since calculated value of F = 9.303 is greater than critical value of F = 2.575:

Reject H0

TO FIND:-f)Find the 95% confidence interval for the difference between treatment 2 and 3.

now we have that as

n1 = 10 n2 = 8

1 = 6.0 2 = 4.25

s1 = 1.6330 s2 = 1.5811   

= 0.05

so now

finding the Pooled Standard Deviaion

Pooled Standard Deviaion is given by:

df = 10+8 - 2 = 16

=0.05

From Table, critical values of t = 2.12

Confidence Interval:

So,

Answer is:

(0.131. 3.369)

all values of the confidence interval are positive:

we conclude that treatments 2 and 3 are different.

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