A marine biologist would like to estimate the mean lifespan of all Florida manatees . The mean lifespan of a random sample of 53 Florida manatees was found to be 56.5 years. The standard deviation of the lifespans of all Florida Manatees is known to be 9.5 years . Using an 80% confidence level , determine a confidence interval for the mean lifespan of all Florida Manatees. Report the confidence interval using interval notation. Round solutions to two decimal places, if necessary . An 80% confidence interval is given by Suppose the population standard deviation was unknown, but the marine biologist found the standard deviation of the lifespan of the sample of 53 Florida manatees was 10.7 years (along with the sample mean of 56.5 years). Determine a 80% confidence interval for the mean lifespan of all Florida manatees using this new information An 80% confidence interval is given by
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 + ...
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