Which of the following is/are true?
Answer(s): H
Note that the mode is not affected by outliers unless an extreme value occurs frequently. In such a case, it is likely that the observed data contain large errors and hence, it must be reexamined. The median of a set with odd number of observations equals the "middle" observation. If the number of observations is even, the median is the mean of the two middle observations. Thus, II is false.Finally, there is no reason for a rule like (IV) to hold.
Consider the following three investments with annual compounding:Present value years interest rate1.$22,500 56% per year2.$10,000 75% per year3.$15,000 38% per yearThe future values of the 3 investments, at the ends of their investment periods, are:
Answer(s): C
Future value = Present value*(1+r)^N for annual compounding. Therefore, Present value years rate Future value1.22,500 56% 22,500*(1.06)^5 = 30,1102.10,000 75% 10,000*(1.05)^7 = 14,0713.15,000 38% 15,000*(1.08)^3 = 18,896Note that the future value must always be greater than the present value.
________ states the range over which a population parameter likely lies.
A confidence interval gives a range of values within which there is a high probability that the population parameter occurs.
In graphs of return performance, which of the following scales is commonly used?
Answer(s): B
Historical returns are often graphed using a semi-logarithmic scale, where equally-large y-axis movements correspond to equally-large percentage changes. An arithmetic scale, on the other hand, has equally-large y- axis movements corresponding to equally-large arithmetic changes. So on an arithmetic scale, the vertical movement for a price change from 100 to 110 is just as large as the vertical movement from 10,000 to 10,010.This is widely considered a distortion (if you are considering rates of return), so the semi-logarithmic scale is used instead.
A researcher has a sample of 900 observations from a population whose standard deviation is known to be 3,381. The mean of the sample is calculated to be 465.2. The null hypothesis is stated as Ho: mean < 200. The p-value in this case equals ________.
Answer(s): D
To test the hypothesis, you need to calculate the smallest z-statistic since the null hypothesis is unidirectional and to the left. This makes it the hardest to reject the null and you should always use the most stringent criterion for rejecting the null. After all, the null is the hypothesis maintained to be true by default and only a sufficient weight of evidence should be used to reject that view. The smallest z-statistic under the null is calculated to be (465.2 - 200)/(3381/(900^.5)) = 2.35. The right-tailed probability of observing a z-statistic which is at least as big as 2.35 equals 1.0 - 0.9906 = 0.0094 = 0.94%. This is the p-value of the right-tailed test in this sample.
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