The article “Application of Surgical Navigation to Total Hip Arthroplasty” (T. Ecker and S.Murphy, Journal of Engineering in Medicine, 2007:699–712) reports that in a sample of 123 hipsurgeries of a certain type, the average surgery time was 136.9 minutes with a standard deviationof 22.6 minutes.a) Find a 95% confidence interval for the mean surgery time for this procedure.b) Find a 99.5% confidence interval for the mean surgery time for this procedure.c) A surgeon claims that the mean surgery time is between 133.9 and 139.9 minutes. Withwhat level of confidence can this statement be made?d) Approximately how many surgeries must be sampled so that a 95%confidence intervalwill specify the mean to within ±3 minutes?e) Approximately how many surgeries must be sampled so that a 99%confidence intervalwill specify the mean to within ±3 minutes?

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 + ...