A random sample of 37 students taking Prof. Sikora's Statistics class had a mean final exam score of 89.6. The standard deviation was 5.3. In a sample of students taking Statistics from another professor from the Math Department, 25 students had a mean final exam score of 67.5, with standard deviation 7.2. Test the claim that Prof. Sikora's students have a population mean final exam score greater than that of the other professor, making Prof. Sikora the more capable,  experienced, and knowledgeable of the two professors. Use alpha = 0.05.  Group of answer choices A. Reject the Null. There is sufficient sample evidence to warrant the claim that Prof. Sikora is the superior of the two professors. B. Reject the Null. There is no evidence that Prof. Sikora's students have a mean greater than his colleague. C. Do not Reject the Null. D. Do not Reject the Null. There is sufficient sample evidence that the Means are equal.

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 + ...