Answered: Problem 1: Acme Trucking claims the…

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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Problem 1: Acme Trucking claims the average hourly salary of its mechanics is $9.25, with a standard deviation of $1.55. An employment agency researching local businesses randomly samples 81 mechanics and finds that they have an average hourly salary of $8.95. The employment agency suspects that the average salary given by Acme might be inaccurate, and the true average is lower. Use a 1% level of significance to test this theory. Let x be a random variable representing the hourly salary of mechanics. State the null and alternative hypotheses using x to be the mean of x. X X Assuming x is true, compute the test statistic for the results of the given sample. Should you reject, or fail to reject, the null hypothesis? Problem 2: Determine the correct hypothesis test to use and complete the test. Boys of a certain age are known to have a mean weight of x pounds. A complaint is made that the boys living in a municipal children's home are underfed. As one bit of evidence, x boys (of the same age) are weighed and found to have a mean weight of x pounds. It is known that the population standard deviation σ is 11.6 pounds and that its distribution is normal. Based on the available data, what should be concluded concerning the complaint? (Use a 5% level of significance) An insurance company advertises that it takes 21 days on average to process a claim, with a standard deviation of 8 days. A random sample of 35 customers who filed a claim had an average time of 24 days to process the claims. Use a 1% level of significance to test if this indicates that the average process time is longer than 21 days. It is assumed that the mean systolic blood pressure is x. In the Honolulu Heart Study, a sample of x people had an average systolic blood pressure of x with a standard deviation of x. Is the group significantly different (with respect to systolic blood pressure) from the regular population? Test with a 1% level of significance. Marketers believe that 92% of adults in the United States own a cell phone. A cell phone manufacturer believes that number is actually lower. 200 American adults are surveyed, of which, 174 report having cell phones. Use a 5% level of significance to test

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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