[SOLVED] Statistics - Differance in mean problem

• Nov 26th 2009, 01:19 AM
dhammikai
[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
• Nov 26th 2009, 06:31 AM
novice
Quote:

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 $\displaystyle H_0:\mu_1=\mu_2$ for no difference between two machines, and $\displaystyle h_1:\mu_1 \neq \mu_2$ for there is significant difference between the two, using two tailed-test. In all tests, if $\displaystyle -z_{0.05} < z > z_{0.05}$, reject $\displaystyle H_0$; otherwise accept or withhold your decision.
• Nov 26th 2009, 07:16 AM
matheagle
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.
• Nov 26th 2009, 07:19 AM
matheagle
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
• Nov 26th 2009, 05:50 PM
dhammikai
Thanks
Hi, I gut a answer now thanks matheagle, novice for excellent explanations!(Clapping)
• Nov 26th 2009, 06:22 PM
matheagle
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...

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

vs.

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