Answered: Management claims the mean income for…

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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Management claims the mean income for all senior-level assembly line workers
at 3M equals $700 a week. An employee decided to test this claim believing it
is different from $700.
a. State the hypotheses for this test, and make a conclusion to the test based
upon the confidence interval below. What level is this test?
99% CI of µ: (631.354, 650.868)
b. Suppose management claimed that 60% of senior-level assembly line workers at 3M is greater than $650 a week. An employee created a 95% confidence
interval of the proportion of senior-level assembly line workers using a random
sample of 50 workers. Their confidence interval is below. Based off the confidence interval, is it valid to conclude that less than 60% of workers get paid
more than $650 a week? Why or why not?(Hint: what is the standard error of
a z-test and what is the standard error of a confidence interval for proportions?)

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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