Question

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.

Answer 1

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