# Math Help - [SOLVED] Statistics - Differance in mean problem

1. ## [SOLVED] Statistics - Differance in mean problem

Hi, please give me a help to find the answer for the following statistic problem,

As a production manager suppose you want to check whether the 3 filling
machines have different mean filling times. If you have assign 15 similarly trained &
experienced workers, 5 per machine, at the 5% level of significance, is there a
difference in mean filling times?
Machine 1 Machine 2 Machine 3
25.40 23.40 20.00
26.31 21.80 22.20
24.10 23.50 19.75
23.74 22.75 20.60
25.10 21.60 20.40

See the attached picture for better understanding of the problem

2. Originally Posted by dhammikai
Hi, please give me a help to find the answer for the following statistic problem,

As a production manager suppose you want to check whether the 3 filling
machines have different mean filling times. If you have assign 15 similarly trained &
experienced workers, 5 per machine, at the 5% level of significance, is there a
difference in mean filling times?
Machine 1 Machine 2 Machine 3
25.40 23.40 20.00
26.31 21.80 22.20
24.10 23.50 19.75
23.74 22.75 20.60
25.10 21.60 20.40

See the attached picture for better understanding of the problem
You can compare two machines at a time by setting $H_0:\mu_1=\mu_2$ for no difference between two machines, and $h_1:\mu_1 \neq \mu_2$ for there is significant difference between the two, using two tailed-test. In all tests, if $-z_{0.05} < z > z_{0.05}$, reject $H_0$; otherwise accept or withhold your decision.

3. You should run an F test via ANOVA on this to test all three means at the same time.
I just found this
ANOVA Test
I'm not sure if it's any good, but the idea is correct.

4. Mean1 24.93 Variance1 1.0648
Mean2 22.41 Variance2 1.483
Mean3 20.59 Variance3 0.9205
Variation Between 23.7486667 Variation Within 1.1561

F-Statistic 20.5420523 P-Value 0.00063
Conclusion Very strong evidence against the null hypothesis

5. ## Thanks

Hi, I gut a answer now thanks matheagle, novice for excellent explanations!

6. I would not do a Bonferroni test, where you test pairs of means.
http://www.itl.nist.gov/div898/handb...on4/prc473.htm
You should test...

$H_0: \mu_i=\mu_j$ for all i,j

vs.

$H_a: \mu_i\ne\mu_j$ for some $i\ne j$