A cumulative frequency distribution on days absent during a calendar year by employees of a manufacturing company is shown below.Days Absent Cumulative Number of Employees0 - 2603 - 5316 - 8149 - 11612 - 142How many employees were absent more than five days?
Answer(s): A
The cumulative number for class 6-8 will give us the number of people absent more than five days; 14.
Tran Holten, a quantitative analyst with Smith, Kleen & Beetchnutty Brokerage, has just been informed of an important error in one of his recent statistical endeavors. Specifically, in one hypothesis test, Mr. Holten rejected a null hypothesis that later was proven to be true. Which of the following best describes this type of error in hypothesis testing? Further, if the confidence level of the test were increased, would the probability of this error increase, decrease, or remain unchanged?
In this example, Tran Holten has incorrectly rejected a null hypothesis. This type of error in hypothesis testing is called a Type I error. In hypothesis testing, the Type I error is given much more attention than the Type II error.In most hypothesis tests, the probability of a null hypothesis is equal to the significance level of the test. A significance level of 0.01, for example, indicates that a 1% chance exists that the null hypothesis will be rejected when it is indeed true. Another way to think of the probability of a Type I error is to observe the following relationship:{Probability of a Type I error = (1 - confidence level)}.For example, a confidence level of 95% leaves a 5% probability of a Type I error occurring. If this confidence level were to increase to say, 98%, then the probability of a Type I error would reduce to 2%. As you can see, there is a relationship between the confidence level of a test and the probability of a Type I error. If the confidence level of the test in this example were to increase, then the probability of a Type I error would decrease.
You believe the stock of Microsquish reflects a 90% chance of a dismissal of its contractual liability suit. If the suit is dismissed, you expect the stock of Microsquish and its partner, AWOL, to rise. If the suit is not dismissed, both will fall in price. However, you think that AWOL's stock only reflects a 60% chance of dismissal of this suit. What strategy would be optimal?
Answer(s): D
This is an example of the investment consequences of inconsistent probabilities. If the true probability of a lawsuit dismissal is only 60%, then AWOL's stock is fairly valued, and Microsquish is overvalued. If the true probability is 90%, then Microsquish is fairly valued, and AWOL is undervalued. Your can thus construct a profitable risk-free strategy. You should buy AWOL, because at worst, the stock will be fairly valued. At best, it is undervalued. You could also simultaneously short Microsquish, because at best, it is fairly valued; there is a chance that it is overvalued. Note that this example ignores all other factors other than the lawsuit.
If the correlation coefficient between two variables equals zero, what can be said of the variables X and Y?
Answer(s): B
r ranges from -1 to +1. The closer it is to -1 or +1, the stronger the relationship. Closer it is to zero, the weaker.
How much must you deposit today in order to withdraw $500 in 1 year, $700 in 3 years and $500 in 4 years,assuming your money earns 6.5% per year, compounded annually?
Answer(s): E
Solve this question by working 3 compound interest problems. On the BAII Plus, press 1 N, 6.5 I/Y, 0 PMT, 500 FV, CPT PV, which yields $469.48. Then press STO 1. Then press 3 N, 700 FV, CPT PV, which yields $579.49. Then press + RCL 1 = STO 1. Then press 4 N, 500 FV, CPT PV, which yields $388.66. Then press + RCL 1 = to see the answer. On the HP12C, press 1 n, 6.5 i, 0 PMT, 500 FV, PV. Then press STO 1. Then press 3 N, 700 FV, PV. Then press RCL 1 + STO 1. Then press 4 n, 500 FV, PV. Then press RCL 1 + to see the answer. Note that the answer will be displayed as a negative number. Make sure the BAII Plus has the P/Y value set to 1.
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