Answered: Consider the dataset refering to screw…

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

Consider the dataset refering to screw lengths. (Is it possible to ask a question that has parts a and b to it if not I will ask separately thank you)

a) Use a 0.05 significance level to test the claim that the screws have a mean length equal to 3/4 in. (or 0.75 in.), as indicated on the package labels. Do the screw lengths appear to be consistent with the package label? (Assume that the standard deviation of the population is unknown). Find the p-value.

b) Use a 0.05 significance level to test the claim that the standard deviation is greater than 0.01.

Write down the hypothesis, the sample mean and standard deviation, the test statistic, the critical values, and the conclussion.

Dataset:

Length of screws
0.757
0.723
0.754
0.737
0.757
0.741
0.722
0.741
0.743
0.742
0.740
0.758
0.724
0.739
0.736
0.735
0.760
0.750
0.759
0.754
0.744
0.758
0.765
0.756
0.738
0.742
0.758
0.757
0.724
0.757
0.744
0.738
0.763
0.756
0.760
0.768
0.761
0.742
0.734
0.754
0.758
0.735
0.740
0.743
0.737
0.737
0.725
0.761
0.758
0.756

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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