Question

Employees at a company produced refrigerators on three shifts. Each shift recorded their quality stats below. A unit was considered defective if it at least one part was assembled wrong or was missing. Management believes that quality depends on the the shift it was produced. Test the claim that shifts are independent of quality using chi-square at alpha = 0.05. SHOW YOUR WORK

1st shift 2nd Shift 3rd Shift

Defective 7 5 9

Good 33 35 31

1st 2nd 3rd

defective

good

quality shift fo fe fo - fe (fo - fe )2 (fo - fe )2 ÷ fe

Is there enough evidence that quality of refrigerators depends on the shift it is produced?

Answer 1

	Observed Frequencies
	0
0	1	2	3				Total
Defective	7	5	9				21
Good	33	35	31				99

	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	1	2	3				Total
Defective	40*21/120=7	40*21/120=7	40*21/120=7				21
Good	40*99/120=33	40*99/120=33	40*99/120=33				99

	(fo-fe)^2/fe
Defective	0.000	0.571	0.571
Good	0.000	0.121	0.121

Ho: given two variable are independent
H1: Given two variables are not independent

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   1.385                          
                              
Level of Significance =   0.05                          
Number of Rows =   2                          
Number of Columns =   3                          
Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 3- 1 ) =   2                          
                              
p-Value =   0.5003   [Excel function: =CHISQ.DIST.RT(χ²,df) ]                      
Decision:    p value > α , do not reject Ho  

                      
We can conclude that  the quality of refrigerators does not depends on the shift it is produced

Thanks in advance!

revert back for doubt

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