Question

given that random samples of process A produced 10 defective and 30 good units, while process B produced 25 defectives out of 60 units. Using the Chi square test, what is the probability that the observed value of chi swuare could result under the hypothesis that both processes are operating at the same quality level?

Answer 1

H₀ : Both process are operating at the same quality level.

H_a : Processes are not operating at same quality level.

Here the observed table is

	Defective	Good	Total
Process A	10	30	40
Process B	25	35	60
Total	35	65	100

So, here

expected observed value of Process A and defective = 35 * 40/100 = 14

expected observed value of Process A and Good = 65 * 40/100 = 26

expected observed value of Process B and defective = 35 * 60/100 = 21

expected observed value of Process B and Good = 65 * 60/100 = 39

Expected table

	Defective	Good	Total
Process A	14	26	40
Process B	21	39	60
Total	35	65	100

Here chi-square value

= (10 - 14)²/14 + (30 - 26)²/26 + (25 - 21)²/21 + (35 - 39)²/39 = 2.9304

so here degree of freedom = dF = 1

P - value = CHIDIST(2.9304, 1) = 0.0869 > 0.05

so we would fail to reject the null hypothesis and conclude that Both process are operating at the same quality level.