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. 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.

$\backslash$table$[[$Memory Location,$1,2,3,4,5],[\backslash$table$[[$Number of$],[$Transactions$]],82,,,,],[\backslash$table$[[$Number of$],[$Reported Errors$]],11,100,74,92,102],[$Seported$,,,,,]]$

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 degrees of frepdom of the test statistic is