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Statistics - Chi-Squared Test for independence

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Question :
A quality control engineer wants to compare the production process of parts manufactured by four different companies. The engineer randomly samples a total of 270 parts from the four companies and summarizes the results in the following table. Based upon the results of the sample, can the quality control engineer conclude that part quality and manufacturer are independent at level of significance of 1%

Part Quality Co. A Co. B Co. C Co. D Row Total
Defective 8 8 10 9
Non-Defective 60 65 60 50
Column Total

a) Formulate the hypothesis
b) State the decision rule
c) Calculate Chi-Square statistic
d) Determine the conclusion and answer the question

For the full description of the question, please see the attached question file.
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Solution Preview

Null Hypothesis :
H0 : part quality and manufacturer are independent of each other
Alternate Hypothesis:
H1 ...

Solution Summary

In the solution for the posted problem on Chi-Squared Test for testing the Relationship between attributes( Test of Independence), the solution to the posted problem is given with step by step working and simplification in such a way that the student could easily understand the solution procedure and could use the solution of this problem as a model solution to solve other similar problems.

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2. The issue of how much should be spent to solve particular U.S. social problems is a complex matter and people have diverse and conflicting ideas on these issues. Race and social class have an impact on how people perceive the extent of government spending. The 2006 GSS contains several questions on these topics. For this exercise, we present race and the variable NATFARE which asked whether we were spending too much, too little, or the right amount of money to address welfare.

Spending on welfare Race of respondent
White Black Hispanic Total
Too little 128 41 21 190
About right 197 32 21 250
Too much 185 31 19 235
Total 510 104 61 675

4. We continue our analysis from Exercise 2, this time examining the relationship between social class (CLASS) and spending on welfare (NATFARE).
a) What is the number of degrees of freedom for this table?
b) Calculate the chi-square. Based on an alpha of 0.01, do you reject the null hypothesis? Explain the reason for your answer.

Social class
Lower class Working class Middle class Upper class Total
Too little 23 92 76 8 199
About right 12 113 133 10 268
Too much 12 127 99 7 245
Total 47 332 308 25 712

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