Answered: The Discovery Medical Aid Board wanted…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

The Discovery Medical Aid Board wanted to find out if the mean time to settle medical claims of members differs between two major medical schemes – the Green-Aid Fund and the Explorer Blue Fund. Fifty Green-Aid Fund medical claims received were randomly selected and monitored, and the sample mean time to settlement was 20.8 days. Assume a population standard deviation of 8.2 days for settlement times of Green-Aid Fund claims. For a random sample of 45 Explorer Fund medical claims received, the average time to settlement was 18.4 days. Assume a population standard deviation of 6.3 days for settlement times of Explorer Blue Fund claims. Assume settlement times are normally distributed. Can the Discovery Medical Aid Board conclude that the Green-Aid Fund settles claims slower, on average, than the Explorer Blue Fund? Formulate the null and alternative hypothesis and test this hypothesis at the 7% significance level. What conclusion can be drawn?

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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