1. You have the following random samples containing information on annual income (measured in thousands) and marital status for individuals living in urban and rural areas.   Urban annual income Urban Married Rural annual income Rural Married 33 Yes 22 Yes 56 Yes 81 Yes 88 No 19 No 43 No 26 Yes 28 Yes 38 Yes 42 Yes 101 No 105 No 31 Yes 90 Yes 29 No 21 Yes 35 Yes 47 No 39 Yes 57 No 66 Yes 19 No 99 No 118 Yes 18 Yes 77 Yes 92 Yes 50 Yes 65 Yes 31 No 48 No   The samples have the following standard deviations: S Urban = 30.41 S Rural= 29.26   Test the hypothesis that there is a difference in mean income between people living urban areas and rural areas. Use a 5% level of significance. Test the hypothesis that there is a difference in the proportion of people married between those living in urban areas and those living in rural areas. Use a 5% level of significance.

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 + ...