In a study conducted to monitor the quality of eyeglasses purchased over the Internet, 154 pairs of glasses were received from individual orders placed with several different online vendors. The lenses were subject to both an optical analysis and a standard impact test. A pair of glasses passes a test only if both lenses pass. The outcomes for these two tests are summarized as

(a) Perform a x2 test of dependence. Take a = .01.
(b) This is a very unusual case. Does it prove independence? Explain.

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Number of Pairs of Glasses Failed Optical OpticalTotal 34 I0 Passed Passed Impact Failed Impact 85 25 119 35 Total 110 154