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Description: A manufacturer makes steel rods that are supposed to have a mean length of 50 centimeters. A retailer suspects that the bars are being produced too short. A sample of 46 bars is taken and their mean length is determined to be 51 centimeters with a st

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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A manufacturer makes steel rods that are supposed to have a mean length of 50 centimeters. A retailer suspects that the bars are being produced too short. A sample of 46 bars is taken and their mean length is determined to be 51 centimeters with a standard deviation of 3.6 centimeters. Using a .01 significance level, test the retailers claim that the population mean is less than 50 centimeters.

1. State the null hypothesis H0:

2. State the alternative hypothesis H1:

3. What is the test statistic used for the test (z or t) and it’s value (round to 2 places)

4. State the significance or alpha (α) level

5. Determine the p-value. (round to 4 places)

6. Do you or do you not reject the null hypothesis? Why?

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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