The mayor is interested in finding a 98% confidence interval for the mean number of pounds of trash per person per week that is generated in the city. The study included 204 residents whose mean number of pounds of trash generated per person per week was 35.4 pounds and the standard deviation was 8.2 pounds. Round answers to 3 decimal places where possible. a. With 98% confidence the population mean number of pounds per person per week is between____  and ____  pounds. b. If many groups of 204 randomly selected members are studied, then a different confidence interval would be produced from each group. About ____ percent of these confidence intervals will contain the true population mean number of pounds of trash generated per person per week and about ___  percent will not contain the true population mean number of pounds of trash generated per person per week.

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 + ...