For each claim, express the original claim in symbolic form. Then identify the null and alternative hypotheses. Use appropriate notation. a) A home security salesperson claims that more than 15% of households are impacted by crime each year. b) In 2017, the mean number of people incarcerated in the United States we 655 per 100,000 people in the national population. A politician claims that the mean in his district is the same as the national mean. c) A machine fills 12-ounce bottles with soda. The machine must have a standard deviation less than or equal to 0.03 ounces to be functioning properly. A technician claims that the machine is working properly

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 + ...