Question

4. Bank Security Report reports that the amount of checks handled by U.S. banks increased from 46 billion to 61 billion between 1983 and 1993. The check fraud also increased. A 1993 ABA survey of 30 midsize banks found a mean loss due to check fraud of $30,433 per bank. Losses at the 30 individual banks ranged from $208 to $400,000 with a standard deviation of $50,000. Conduct a test at α = .05 to see whether the true mean loss due to check fraud in 1993 exceeds $14,100.

Answer 1

Solution

here null hypothesis: Ho: =14100

alternate hypothesis: Ha: >14100

here std error of mean =std deviation/(n)^1/2 =50000/(30)^1/2 =9128.71

therefore test stat t =(X-mean)/std error =(30433-14100)/9128.71=1.7892

for above test stat and (n-1=29) degree of freedom

=T.DIST.RT(1.7892,29) ( Excel function)

; p value =.0042016.

as p value is less then 0.05 level; we reject null hypothesis and conclude that  true mean loss due to check fraud in 1993 exceeds $14,100.