The two intervals (114.9, 115.7) and (114.6, 116.0) are confidence intervals (calculated using the same sample data) for ? = true average resonance frequency (in hertz) for all tennis rackets of a certain type. (a) What is the value (in hertz) of the sample mean resonance frequency? (Hint: Where is the confidence interval centered?)  ________hertz (b) The confidence level for one of these intervals is 90% and for the other it is 99%. Which one has a confidence level of 99%?   (114.9, 115.7) (114.6, 116.0)     It is impossible to tell which is which.   How can you tell? The 99% confidence interval should be wider than the 90% confidence interval.   The center of the 99% confidence interval should be greater than the center of the 90% confidence interval.       The 99% confidence interval should be narrower than the 90% confidence interval.   The center of the 99% confidence interval should be less than the center of the 90% confidence interval.   It is impossible to tell which is which

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 + ...