SCENARIO 12-4
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.
The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ.
-Referring to Scenario 12-4,the calculated value of the test statistic is
A)-0.1777
B)-0.0185
C)1.2068
D)1.5190

Question

SCENARIO 12-4
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.
  The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ.
-Referring to Scenario 12-4,the calculated value of the test statistic is
A)-0.1777 
B)-0.0185 
C)1.2068 
D)1.5190

Quizplus · Accepted Answer

In order to test whether the proportions of errors in transactions assigned to each memory location differ, we can use a chi-square goodness-of-fit test. The null hypothesis is that the proportions are equal across all memory locations, and the alternative hypothesis is that at least one proportion differs. We can calculate the test statistic as the sum of (observed count - expected count)^2 / expected count across all memory locations. Using this formula and the given data, we get a test statistic of 1.2068. This corresponds to a p-value of approximately 0.87, which is much larger than any reasonable level of significance. Thus, we fail to reject the null hypothesis and conclude that there is not enough evidence to conclude that the proportions of errors differ across memory locations.

SCENARIO 12-4 A Computer Used by a 24-Hour Banking Service Is Supposed