Statistic

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TABLE 12-3

A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of 5 memory locations. A check at the end of a day's transactions gave the counts shown in the table to each of the 5 memory locations, along with the number of reported errors.

Memory Location: 1 2 3 4 5
Number of Transactions: 82 100 74 92 102
Number of Reported Errors 11 12 6 9 10

The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ.

(a) Referring to Table 12-3, the degrees of freedom of the test statistic is
A) 4
B) 8
C) 10
D) 448

(b) Referring to Table 12-3, the critical value of the test statistic at 1% level of significance is
A) 7.7794
B) 13.2767
C) 20.0902
D) 23.2093

(c) Referring to Table 12-3, the calculated value of the test statistic is
A) -0.1777
B) -0.0185
C) 1.4999
D) 1.5190

(d) Referring to Table 12-3, at 1% level of significance:
A) there is sufficient evidence to conclude that the proportions of errors in transactions assigned to each of the 5 memory locations are all different.
B) there is insufficient evidence to conclude that the proportions of errors in transactions assigned to each of the 5 memory locations are all different.
C) there is sufficient evidence to conclude that the proportion of errors in transactions assigned to each of the 5 memory locations are not all the same.
D) there is insufficient evidence to conclude that the proportion of errors in transactions assigned to each of the 5 memory locations are not all the same.

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