In which of the following scenarios will conducting a two-sample t-test for means be appropriate? CHECK ALL THAT APPLY. A. To test if there is a difference between the mean annual income of British Columbians and a known national mean. B. To test if the mean annual income of Ontarians is higher than that of British Columbians. C. To test if the proportion of low-income families is higher than that of high-income families in British Columbia. D. To test if there is a difference between the proportion of low-income families in British Columbia and a known national proportion. E. To test if there is a difference between the mean annual income of male British Columbians and that of female British Columbians. F. To test if there is a difference between the mean annual income of husbands and that of wives in Canada. G. None of the above

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...