The mean voltage and standard deviation of 7 batteries from each manufacturer were measured. The results are summarized in the following table. Manufacturer A Sample mean voltage (millivolts): 128 Sample standard deviation (millivolts): 2 Manufacturer B Sample mean voltage (millivolts): 125 Sample standard deviation (millivolts): 5 What type of hypothesis test should be performed? Unpaired t-test Two-tailed z-test Left-tailed z-test Paired t-test What is the test statistic? What is the number of degrees of freedom? Does sufficient evidence exist to support the claim that the voltage of the batteries made by the two manufacturers is different at the α = 0.01 significance level? Yes No

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 + ...