The director of a medical hospital feels that her surgeons perform fewer operations per year than the national average of 211. She selected a random sample of 15 surgeons and found that the mean number of operations they performed was 210.4. The standard deviation of the sample was 3.8. Is there enough evidence to support the directors feelings at (alpha) = 0.05? Assume that the population is approximately normally distributed. Use the critical value method and tables. A. State the hypotheses and identify the claim with the correct hypothesis. B. Find the critical value(s). C. Compute the test value. D. Make the decision. E. Summarize the results.

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 + ...