Hypothesis Test for Balanced Load on 6 I/O Channels - N = 150

[TomJerry]

Question : A computer system has 6 I/O channels and the system personnel are reasonably certain that the load on channels is balanced. If X is random variable denoting the index of the channel to which a given I/O operations is directed , that its pmf is assumed to be uniformly distributed. Out of N=150 I/O operation onserved, the number of operations directed to various channels were:
n₀ = 22 ; n₁ = 23 ; n₂ = 29 ; n₃ = 31 ; n₄ = 26 ; n₅ = 19

Test the hypothesis that the load on channels is balanced at 5 percent level of significance.

Solution
I have used the $$\chi$$² = (O-E)² / E

where O - obsevred and E is expected

Is this correct or should i be using some other method

 

[SW VandeCarr]

Question :

where O - obsevred and E is expected

Is this correct or should i be using some other method

You can use the chi square test $$\chi^2=\sum (O-E)^2/E$$ Do you know how to get E?

 

[TomJerry]

You can use the chi square test $$\chi^2=\sum (O-E)^2/E$$ Do you know how to get E?

I have taken all the E = $$\Sigma$$x_i/6

Is that correct?

 

[SW VandeCarr]

I have taken all the E = $$\Sigma$$x_i/6

Is that correct?

Yes. If each I/O is taken as equally probable, 150/6=25=E.

 

[TomJerry]

Yes. If each I/O is taken as equally probable, 150/6=25=E.

Thanks

 

[SW VandeCarr]

If you're being sarcastic, why did you ask for confirmation in the first place?