In this lab you investigate check amounts collected from two different bank tellers (the data is in a file attached to this assignment). Each sample is a simple random sample of checks collected over a one week period. The manager at the bank has become concerned about check fraud. You are to analyze the data to determine if there is cause for concern. Benford's law states that the leading digit of the check amounts should be a 1 roughly 30% of the time. To complete this lab, please submit answers to each of the following questions. Make sure you number your answers to each question and describe how you are getting each answer. If you are using a calculator or Excel function for a calculation, include the name of that function. 1. Record the leading digit of the check amounts for both data sets. For example, if a check amount was $452, the leading digit is 4.
2. Recording the leading digits of checks and counting the number of leading digits that are a "T" for each teller is a binomial experiment. Let's call Teller A's checks one set of sample data and Teller B's checks a second sample. For each sample:
1. How many trials are there?
2. Are the trials independent?
3. What is considered to be a success, what is considered to be a failure?
4. What is the probability of success, the probability of failure? (Hint: Reread the statement about Benford's Law.)
3. Using what you know about finding probabilities for binomial distributions, find the probability of getting exactly the number of ones you counted in each sample.
4. We can calculate a range of usual values to determine if our sample sets have an unusual number of I's in them. To do this, first find the mean and standard deviation for a sample of 50 check amounts. Remember that looking for "1" in these samples is a binomial distribution. Please list your answers for the mean, standard deviation and the range of usual values.
5. Determine if the number of ones in each sample is usual or unusual. 6. What can you conclude about the risk of bank fraud happening with Teller A? With Teller B? What should you tell the bank manager?
Teller A Teller B Lead Check Amounts Leading digit 686 103 598 360 Check Amounts 122 199 237 732 424 279 275 124 402 139 467 310 144 794 90 702 277 354 907 383 285 558 955 829 140 12 784 605 375 815 819 740 260 285 151 658 138 399 249 190 294 194 567 162 772 935 161 475 424 957 785 427 49 188 227 338 603 496 541 554 22 744 701 117 175 168 848 423 551 155 234 225 179 251 828 659 32 726 104 659 361 370 235 496 401 46 435 156 427 290 226 906 758 718 50