A technician compares repair costs for two types of microwave ovens (type I and type II). He believes that the repair cost for type I ovens is greater than the repair cost for type II ovens. A sample of 6060 type I ovens has a mean repair cost of $77.22$⁢77.22, with a standard deviation of $22.46$⁢22.46. A sample of 6565 type II ovens has a mean repair cost of $73.73$⁢73.73, with a standard deviation of $10.62$⁢10.62. Conduct a hypothesis test of the technician's claim at the 0.10.1 level of significance. Let μ1μ1 be the true mean repair cost for type I ovens and μ2μ2 be the true mean repair cost for type II ovens. Step 2 of 4 :   Compute the value of the test statistic. Round your answer to two decimal places.

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 + ...