An investment of $100 grows in three years to $221. The investor observes that the annual arithmetic rate of return and the geometric rate of return were the same over this period. The annual arithmetic rate of return must be ________.
Answer(s): A
If the annual geometric rate of return is r, then 100 * (1 + r)^3 = 221. This gives r = 30.26%. Note that the only way the mean will be equal to the geometric mean if every year, the stock experienced a return of 30.26% per year.
If all the data points in a regression lie exactly on a straight line, which of the following is/are true?
Since there is no error in the regression, the R-square equals 1 (100%). The slope coefficient can be any real number, not necessarily 1. The residual error will be zero.
Which of the following answers is false in reference to confidence levels and/or tests of significance? Choose the best answer.
The confidence interval for a test with a 5% level of significance is smaller than the confidence interval for a 1% significance level. Remember that the significance level is typically set equal to the probability of a Type I error, which is defined as the act of incorrectly rejecting the null hypothesis. In hypothesis testing, the significance level is denoted by the Greek letter alpha. As the level of confidence increases, then the confidence interval will increase. This will be mirrored by a decrease in the alpha coefficient (i.e. the probability of a Type I error) for the hypothesis test. The remaining answers are correct.
If 68% of the observations of a bell-shaped, symmetrical frequency distribution fall between -20 and + 60, the mean and the standard deviation of the distribution are:
Answer(s): D
Since the distribution is symmetrical about the mean, the mean is equal to (-20 + 60)/2 = 20. According to the empirical/Normal rule, for a bell-shaped, symmetrical frequency distribution, 68% of the observations lie within one standard deviation of the mean. Therefore, the standard deviation equals 60-20 = 40.
What is the range of values for a coefficient of correlation?
The closer the value to 1 or -1, the stronger the correlation. The sign +/- just shows the direction, not the strength.
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