The recorded inventory balance for Faulk Company was $$1,000,000$ and comprised $2,500$ customer accounts.

Required:

For each of the following independent sets of conditions, determine the appropriate sample size for the audit of Faulk's inventory using classical variables sampling $($mean$-$per$-$unit estimation$).($RIA $=$ risk of incorrect acceptance, RIR $=$ risk of incorrect rejection, $TM=$ tolerable misstatement, $EM=$ expected misstatement, $SD=$ standard deviation.$)($Roundup your answers to the nearest whole numbers.$)$

$\backslash$table$[[,,$Sample Size$],[$a$.,$RIA$=5\%,$RIR$=5\%,TM=$$$50,000,EM=$$$20,000,SD=$$$40.,],[$b$.,$RIA$=10\%,$RIR$=5\%,TM=$$$50,000,EM=$$$20,000,SD=$$$40.,],[$c$.,$RIA$=10\%,$RIR$=10\%,TM=$$$50,000,EM=$$$20,000,SD=$$$40.,],[$d$.,$RIA$=5\%,$RIR$=5\%,TM=$$$30,000,EM=$$$20,000,SD=$$$40.,],[$e$.,$RIA$=5\%,$RIR$=5\%,TM=$$$50,000,EM=$$$10,000,SD=$$$40.,],[$f$.,$RIA$=5\%,$RIR$=5\%,TM=$$$50,000,EM=$$$10,000,SD=$$$30.,]]$

Based on the differences in your calculations, identify the general relationship between different factors and sample size.

$\backslash$table$[[$Relationship between risk of incorrect acceptance and sample size,$],[$Relationship between risk of incorrect rejection and sample size,$],[$Relationship between tolerable misstatement and sample size,$],[$Relationship between expected misstatement and sample size,$],[$Relationship between standard deviation and sample size,$]]$