For each problem, complete the following steps:(a) State the null and alternative hypothesis.(b) Determine which distribution to use for the test statistic, and state the level of significance. (c) Calculate the test statistic.(d) Draw a conclusion and interpret the decision. A manufacturer is responsible for making barrels used to store crude oil, which are designed to hold exactly 55 gallons of oil. As part of a routine quality check, a factory manager randomly tests 27 barrels off the assembly line and finds that their mean capacity is 54.7 gallons with a standard deviation of 0.8 gallons. Can the manager say with 99% confidence that the requirements are being met? Assume that the population distribution is approximately normal.

State the hypotheses. That is, the true population mean equals 55. That is, the true population…

Answered: For each problem, complete 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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For each problem, complete the following steps:
(a) State the null and alternative hypothesis.
(b) Determine which distribution to use for the test statistic, and state the level of significance.
(c) Calculate the test statistic.
(d) Draw a conclusion and interpret the decision.

A manufacturer is responsible for making barrels used to store crude oil, which are designed to hold exactly 55 gallons of oil. As part of a routine quality check, a factory manager randomly tests 27 barrels off the assembly line and finds that their mean capacity is 54.7 gallons with a standard deviation of 0.8 gallons. Can the manager say with 99% confidence that the requirements are being met? Assume that the population distribution is approximately normal.

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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