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It is a striking fact that the first digits of numbers in legitimate records often follow a distribution known as Benford's Law, shown below.
First digit 1 2 3 4 5 6 7 8 9Proportion 0.285 0.175 0.113 0.088 0.058 0.06 0.031 0.039 0.151
Fake records usually have fewer first digits 1, 2, and 3. What is the approximate probability, if Benford's Law holds, that among 1234 randomly chosen invoices there are no more than 673 in amounts with first digit 1, 2, or 3? (Round your answer to four decimal places.)
Is there evidence that population mean amount is different form 8.17 ounces? (Use a 0.05 level of significance.) with sample standard deviation of 0.051 ounce.
Perform a chi-square test on the following data:
You're in charge of an experiment to evaluate a treatment which is advertised as being 90% effective at killing a particular insect. You plan an experiment in which the treatment is tested on 200 insects.
Mark makes it a policy not to buy bananas unless the price is 33 cents or less per pound. What proportion of the time would he buy bananas?
Would you conclude that your data set is approximately normal? If so, what percentage of your data values lie:
The lifetime of a color television picture tube is normally distributed with the mean of 7.8 years and a standard deviation of 3 years.
Test whether there is a statistical difference between the two proportions at the 5% significance level.
Descriptive statistics for given data - Evaluate the range, variance, and standard deviation of the data set. Interpret the results in the context of the real-life setting.
A check of dorm rooms on a large college campuses revealed that 38% had refrigerators, 52 percent had TVs and 21 percent had both a TV and a refrigerator. What's the probability that a randomly selected dorm room has.
Explain your findings (including the logic of comparing within-group to between-group population variance estimates, how each of these is figured, and the F distribution).
For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.3770. Find value of Z? For some value of Z, the probability that a standard normal variable is below Z is 0.2090. Find value of Z?
Given CAPM as the benchmark, is either of the two managers over-performing the market? What if you use the Sharpe Ratio as benchmark? Explain the answer carefully.
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