Given the following hypotheses:   H0: μ = 450 H1: μ ≠ 450   A random sample of 11 observations is selected from a normal population. The sample mean was 456 and the sample standard deviation was 5. Using the 0.10 significance level:   State the decision rule. (Negative amount should be indicated by a minus sign. Round your answers to 3 decimal places.)         Compute the value of the test statistic. (Round your answer to 3 decimal places.)         What is your decision regarding the null hypothesis?   multiple choice Reject Do not reject

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 + ...