A study of compulsive buying behavior conducted a national telephone survey in 2004 of adults aged 18 and over. The total credit card balance had a mean of $3,399 and standard deviation of $5,595 for 100 compulsive buyers and a mean of $2,837 and standard deviation of $6,335 for 1,682 other respondents. Question: Compare the population means using a two-sided significance test (state the hypotheses, calculate a test statistic, estimate the p-value, and make a decision about whether there is enough evidence to reject the null hypothesis if alpha=0.05). If you can’t find a precise p-value, come up with the best estimate possible from the distribution table.

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 + ...