Question

(please i need the answer asap )Computer chips defects are classified according to type of defect and shift on which it was made. The numbers of defects are recorded in the the table below. Do the data present sufficient evidence to indicate that the type of computer chip defect varies with the shift during which they are produced? Test at the 5% level of significance.

	Shift
Type	1	2	3	TOTAL
A	14	25	32	71
B	20	30	16	66
C	44	33	48	125
D	12	4	19	35
TOTAL	90	92	115	297

Answer 1

We are to test, : type of computer chip defect is independent of the shift during which they are produced, versus, : type of computer chip defect is dependent of the shift during which they are produced. Given, .

Now, the observed frequencies are = = (14,20,44,12,25,30,33,4,32,16,48,19). Now, the corresponding expected frequencies are calculated using the formula: (row total * column total)/grand total and the expected frequencies are = = (21.52,20.00,37.88,10.61,21.99,20.44,38.72,10.84,27.49,25.56,48.40,13.55).

Test statistic value = = 20.34.

Critical value = = 12.59, where, r = no. of rows = 4, c = no. of columns = 3.

Since the test statistic value is greater than the critical value, we reject and conclude at 5% significance level that there is enough sample evidence to suggest that the type of computer chip defect varies with (is dependent on) the shift during which they are produced.