and alternative hypotheses Calculate the expected results for the hypothesis test assuming the null hypothesis is true and determine the hypothesis test model , i.e., “cut-off” critical values etc. Formulate the decision rule, i.e., include “one-tail ”left, or “one-tail” right, or “two-tail” determination etc. Determine the experimental outcome. Determine the conclusion, and answer the question(s) posed in the problem, if any. An astronomer is testing the claim that the mean brightness of a certain star is now more than 30 units.  The astronomer is able to get 6 readings on the star during an experiment as shown in the table.  Using a 1% level of significance, does this indicate a new mean brightness of more than 30?

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 + ...