Question

The following is sample information. Test the hypothesis that the treatment means are equal. Use the 0.01 significance level.

Treatment 1	Treatment 2	Treatment 3
9	9	3
8	10	5
4	10	4
9	7	4

a. State the null hypothesis and the alternate hypothesis.

H₀: click to select (The treatment means are not all the same, the treatment means are the same) *pick which answer is correct from the options in the brackets*

H₁:   click to select (The treatment means are not all the same, the treatment means are the same) *pick which answer is correct from the options in the brackets*          

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

Reject H₀ if the test statistic is greater than _______    *fill in _______*

c. Compute SST, SSE, and SS total. (Round the final answers to 3 decimal places.)

SST = ________ *fill in ______*             

SSE = ________ *fill in ______*             

SS total = ________ *fill in ______*

d. Complete the ANOVA table. (Round the SS, MS, and F values to 3 decimal places.)

Source	SS	DF	MS	F
Treatment	______	______	______	_____
Error	_______	_______	_____	n / a
Total	_______	_____	n / a	n / a
*fill in _____, ignore N/A)

e. State your decision regarding the null hypothesis.

click to select (Do not reject, reject )H₀.*pick which answer is correct from the options in the brackets*

Answer 1

a.

Here we define the null and alternate hypothesis as follows:

H0: The treatment means are the same

H1: The treatment means are not all the same.

b.

We reject the null hypothesis if the test statistic is greater than F statistic with level of significance =0.01 and degrees of freedom 2,9

c.yij is the jth treatment corresponding to the ith level i=1,2,3 j=1,2,3,4

=52.670 where Ti0 is the treatment means corresponding to the ith treatment i=1,2,3

and CF is the correction factor = and

=77.670

and SSE= TSS-SST=25.00

d.

Source DF SS   MS F-Value
treatments 2 52.67 26.333 9.48   
Error 9 25.00 2.778
Total 11 77.67

Here MS= SS/DF

e.

here =8.0215

since F value >

we reject the null hypothesis at 99% level of significance.