The university data center has two main computers. The center wants to examine whether computer 1 is receiving tasks which require comparable processing time to those of computer 2. A random sample of 11 processing times from computer 1 showed a mean of 67 seconds with a standard deviation of 15 seconds, while a random sample of 15 processing times from computer 2 (chosen independently of those for computer 1) showed a mean of 58  seconds with a standard deviation of 16  seconds. Assume that the populations of processing times are normally distributed for each of the two computers, and that the variances are equal. Can we conclude, at the 0.05 level of significance, that the mean processing time of computer 1, μ1, is greater than the mean processing time of computer 2, μ2? Perform a one-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. The null hypothesis: H0:   The alternative hypothesis: H1:   The type of test statistic: (Choose one)ZtChi squareF             The value of the test statistic: (Round to at least three decimal places.)   The p-value: (Round to at least three decimal places.)   Can we conclude that the mean processing time of computer 1 is greater than the mean processing time of computer 2?   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 + ...