Instruction 15-5
A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of five memory locations. A check at the end of a day's transactions gave the counts shown in the table to each of the five memory locations, along with the number of reported errors.
$$\begin{array} { | l | l | l | l | l | l | }
\hline \text { Memory Location } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Number of Transactions } & 82 & 100 & 74 & 92 & 102 \
\hline \text { Number of Reported Errors } & 11 & 12 & 6 & 9 & 10 \
\hline
\end{array}$$ The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the five memory locations differ.
-Referring to Instruction 15-5,the calculated value of the test statistic is
A) -0.0185.
B) 1.5190.
C) -0.1777.
D) 1.4999.

Question

Instruction 15-5
A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of five memory locations. A check at the end of a day's transactions gave the counts shown in the table to each of the five memory locations, along with the number of reported errors.
 $$\begin{array} { | l | l | l | l | l | l | } 
\hline \text { Memory Location } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Number of Transactions } & 82 & 100 & 74 & 92 & 102 \
\hline \text { Number of Reported Errors } & 11 & 12 & 6 & 9 & 10 \
\hline
\end{array}$$ The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the five memory locations differ.
-Referring to Instruction 15-5,the calculated value of the test statistic is
A) -0.0185.
B) 1.5190.
C) -0.1777.
D) 1.4999.

Quizplus · Accepted Answer

To test whether the proportions of errors in transactions assigned to each of the five memory locations differ, we can use the chi-squared test of independence. The calculated value of the test statistic is 1.4999. This can be found by calculating the expected counts of errors in each memory location under the assumption of independence and using these counts to calculate the chi-squared statistic. The degrees of freedom for this test are (r-1)(c-1) = (5-1)(2-1) = 4. Using a significance level of 0.05 and a chi-squared distribution table with 4 degrees of freedom, we find the critical value to be 9.488. Since the calculated value of the test statistic (1.4999) is less than the critical value (9.488), we fail to reject the null hypothesis that the proportions of errors in transactions assigned to each of the five memory locations are equal. Therefore, there is insufficient evidence to conclude that the proportion of errors in transactions assigned to each of the five memory locations differ.

Instruction 15-5 a Computer Used by a 24-Hour Banking Service

Instruction 15-5
a Computer Used by a 24-Hour Banking Service