Question

You are the production manager for a part manufacturing company. There are 2 manufacturing locations, plant A and B. you suspect there is a difference in the proportion of rejected parts that are manufactured at Plant A as compared to plant B. for a week you observed:

	Plant A	Plant B	total
Rejected parts	120	80	200
Acceptable parts	1880	1920	3800
	2000	2000	4000

The proportion of rejected parts was 200/4000=5%. If there were no difference between the proportion of rejected parts whether there were manufactured at either plant A or plant B then you would estimate:

	Plant A	Plant B	total
Rejected parts			200
Acceptable parts			3800
	2000	2000	4000

You decide to preform a chi squared test to determine if there is statistically a difference between the proportion of rejected parts manufactured at plant A as compared to the proportion of rejected parts manufactured at plant B.

1. State your null and alternate hypothesis. B) at the 5% level of significance, is there evidence of a difference between the proportions of rejected parts manufactured at plant A as compared to plant B? based on your hypothesis test what is your conclusion? State your conclusion formally.

Answer 1

ou are the production manager for a part manufacturing company. There are 2 manufacturing locations, plant A and B. you suspect there is a difference in the proportion of rejected parts that are manufactured at Plant A as compared to plant B. for a week you observed:

	Plant A	Plant B	total
Rejected parts	120	80	200
Acceptable parts	1880	1920	3800
	2000	2000	4000

The proportion of rejected parts was 200/4000=5%. If there were no difference between the proportion of rejected parts whether there were manufactured at either plant A or plant B then you would estimate:

	Plant A	Plant B	total
Rejected parts	100	100	200
Acceptable parts	1900	1900	3800
	2000	2000	4000

You decide to preform a chi squared test to determine if there is statistically a difference between the proportion of rejected parts manufactured at plant A as compared to the proportion of rejected parts manufactured at plant B.

State your null and alternate hypothesis.

Ho: There is no difference between the proportion of rejected parts manufactured at plant A as compared to the proportion of rejected parts manufactured at plant B.

H1: There is a difference between the proportion of rejected parts manufactured at plant A as compared to the proportion of rejected parts manufactured at plant B.

B) at the 5% level of significance, is there evidence of a difference between the proportions of rejected parts manufactured at plant A as compared to plant B? based on your hypothesis test what is your conclusion? State your conclusion formally.

Calculations
fo-fe
20	-20
-20	20
(fo-fe)^2/fe
4.0000	4.0000
0.2105	0.2105

Data
Level of Significance	0.05
Number of Rows	2
Number of Columns	2
Degrees of Freedom	1
Results
Critical Value	3.841
Chi-Square Test Statistic	8.4211
p-Value	0.0037
Reject the null hypothesis

Calculated chi square 8.421 > critical chi square value 3.841. Ho is rejected.

We conclude that there is a significant difference between the proportion of rejected parts manufactured at plant A as compared to the proportion of rejected parts manufactured at plant B.