You are faced with a counting problem in which you must choose k objects from n total objects. The order of choosing does not matter. The counting method you should use is:
Answer(s): B
The combination, or binomial formula, gives the number of ways that k objects can be chosen from n items, without regard to the order of choosing. The formula is n_C_k = (n choose k) = n! / [k! *(n-k)!].
In a statistical regression estimation, the R-square is found to be 39% and the slope coefficient is -0.3. The percentage of variance of the dependent variable not explained equals ________.
The R-square of the regression measures the amount of variance of the dependent variable explained by the independent variable. This is given to be 39%. Hence, the amount not explained equals 100% - 39% = 61%.
A bell-shaped, symmetrical frequency distribution has a mean of 10. If 16% of the observations in the distribution are negative, what is the coefficient of variation of X?
Answer(s): A
The fraction of observations which are less than zero equals 16% i.e. the fraction of observations which are less than (mean - 10) equals 16% (given). Since the distribution is symmetrical about the mean, this implies that the fraction of observations which are more than (mean + 10) also equals 16%. Thus, the fraction of the observations lying between 0 and 20 equals 1-0.16-0.16 = 0.68. For a bellshaped, symmetrical frequency distribution, 68% of the observations lie within one standard deviation of the mean. Hence, the standard deviation of the distribution equals 10. The coefficient of variation is then equal to standard deviation/mean = 10/10 = 1.
A population consists of all the weights of all defensive tackles on Sociable University's football team. They are:Johnson, 204 pounds; Patrick, 215 pounds; Junior, 207 pounds; Kendron, 212 pounds; Nicko, 214 pounds; and Cochran, 208 pounds. What is the population standard deviation (in pounds)?
Population variance = (Sum of squared deviation from the mean)/N. The mean is 210. Population variance = (36 + 25 + 9 + 4 + 16 + 4)/6 = 94/6 = 15.67. Population standard deviation is the square root of the population variance = 3.958.xx-mean(x-mean)^2204-636215525207-3921224214416208-24
Which measure of dispersion disregards the algebraic signs (plus and minus) of each difference between Xand the mean?
Answer(s): C
The mean deviation is the mean of the absolute values of the deviations from the mean.
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