In an experiment to determine whether there is a systematic difference between the weights obtained with two different scales, 10 rock specimens were weighed, in grams, on each scale. The following data were obtained:SpecimenWeight on Scale1Weight on Scale2113.3613.19216.8016.4339.759.52411.0311.47526.0026.22610.8010.73714.6814.7486.606.72913.0212.951022.2922.64Let μ1 represent the mean weight on Scale 1 and =μd−μ1μ2.Can you conclude that the the mean weight on Scale 1is less than the mean weight on Scale 2? Use the = α0.05 level of significance.(a) State the null and alternate hypotheses.(b) Compute the test statistic.(c) State a conclusion.

The data shows the difference between the weights for two different scales.

Answered: In an experiment to determine whether…

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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In an experiment to determine whether there is a systematic difference between the weights obtained with two different scales, 10 rock specimens were weighed, in grams, on each scale. The following data were obtained:

Specimen	Weight on Scale 1	Weight on Scale 2
1	13.36	13.19
2	16.80	16.43
3	9.75	9.52
4	11.03	11.47
5	26.00	26.22
6	10.80	10.73
7	14.68	14.74
8	6.60	6.72
9	13.02	12.95
10	22.29	22.64

Let μ1 represent the mean weight on Scale 1 and =μd−μ1μ2.
Can you conclude that the the mean weight on Scale 1is less than the mean weight on Scale 2? Use the = α0.05 level of significance.

(a) State the null and alternate hypotheses.

(b) Compute the test statistic.

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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