A frictional research firm has recommended that installation of ATMs will reduce

Question

A frictional research firm has recommended that installation of ATMs will reduce routine bank transaction costs if over 50% of bank's client use it. To test this contention a frictional bank has installed an ATM in its branch. A random sample of 100 bank client are surveyed about the number of times they used the ATM in the past month. The responses are as follows: What is the best estimate of the percentage of clients who do not use the ATM in a month? Construct a 99% confidence interval for this best estimate. Can the bank be confident that installation of ATMs will result in the reduction of transaction costs? How many ATM transactions does the average client make per month? Construct a 95% confidence interval for the mean number of monthly transactions. Is it likely that the population mean is 0.8? Why? Why not?

Explanation / Answer

a) X = 20 , n = 100

p^ = X/n = 0.20

b) 99% confidence interval

z = 2.576

(0.2 - 2.576 * sqrt(0.2*0.8/100) , (0.2 + 2.576 * sqrt(0.2*0.8/100)

=(0.09696,0.30304)

c) yes , bank can be confident as every value in confidence interval is less than 0.5

d)

E(X) = 2

x f p xp 0 20 0.2 0 1 35 0.35 0.35 2 20 0.2 0.4 3 5 0.05 0.15 4 5 0.05 0.2 5 5 0.05 0.25 6 5 0.05 0.3 7 5 0.05 0.35 2

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