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Eyeglassomatic manufactures eyeglasses for different retailers. They test to see how many defective lenses they made...

Eyeglassomatic manufactures eyeglasses for different retailers. They test to see how many defective lenses they made the time period of January 1 to March 31. Table #11.2.4 gives the defect and the number of defects.

Table #11.2.4: Number of Defective Lenses

Defect type

Number of defects

Scratch

5865

Right shaped - small

4613

Flaked

1992

Wrong axis

1838

Chamfer wrong

1596

Crazing, cracks

1546

Wrong shape

1485

Wrong PD

1398

Spots and bubbles

1371

Wrong height

1130

Right shape - big

1105

Lost in lab

976

Spots/bubble - interim

976

Do the data support the notion that each defect type occurs in the same proportion? Test at the 10% level.

Solutions

Expert Solution

null hypothesis: Ho:  each defect type occurs in the same proportion

alternate hypotheiss: Ha:at least one type of defect occur in different proportion

degree of freedom =categories-1 =13-1=12

for 12 df and 0.1 level ; rejection region >18.549

applying chi square goodness of fit test:

observed Expected Chi square
category Probability(p) Oi Ei=total*p R2i=(Oi-Ei)2/Ei
Scratch 1/13 5865.000 1991.615 7533.135
Right shaped - small 1/13 4613.000 1991.615 3450.293
Flaked 1/13 1992.000 1991.615 0.000
Wrong axis 1/13 1838.000 1991.615 11.849
Chamfer wrong 1/13 1596.000 1991.615 78.585
Crazing, cracks 1/13 1546.000 1991.615 99.705
Wrong shape 1/13 1485.000 1991.615 128.870
Wrong PD 1/13 1398.000 1991.615 176.931
Spots and bubbles 1/13 1371.000 1991.615 193.392
Wrong height 1/13 1130.000 1991.615 372.753
Right shape - big 1/13 1105.000 1991.615 394.698
Lost in lab 1/13 976.000 1991.615 517.909
Spots/bubble - interim 1/13 976.000 1991.615 517.909
total 1.000 25891 25891 13476.029

as test statitic 13476.029 is in critical region; we reject null hypothesis.

we have sufficient evidence at 0.1 level to conclude that  at least one type of defect occur in different proportion

milcah answered 1 year ago
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