A systems analyst tests a new algorithm designed to work faster than the currently-used algorithm. Each algorithm is applied to a group of 7373 sample problems. The new algorithm completes the sample problems with a mean time of 24.2824.28 hours. The current algorithm completes the sample problems with a mean time of 26.9726.97 hours. Assume the population standard deviation for the new algorithm is 3.5873.587 hours, while the current algorithm has a population standard deviation of 4.0394.039 hours. Conduct a hypothesis test at the 0.050.05 level of significance of the claim that the new algorithm has a lower mean completion time than the current algorithm. Let μ1μ1 be the true mean completion time for the new algorithm and μ2μ2 be the true mean completion time for the current algorithm.
Step 1 of 4 :
State the null and alternative hypotheses for the test.
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 + ...
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