Scientists and engineers frequently wish to compare two different techniques for measuring or determining the value of a variable. In such situations, interest centers on testing whether the mean difference in measurements is zero. An article reports the accompanying data on amount of milk ingested by each of 14 randomly selected infants. Infant1234567891011121314DD method15091418156115562169174010981198147912811414193421742058TW method14981254132615652000131814101129134211441468160417221528Difference11164235−9169422−31269137137−54330452530Does it appear that the true average difference between intake values measured by the two methods is something other than zero? Determine the P-value of the test, and use it to reach a conclusion at significance level 0.05. Calculate the test statistic and P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.)

From the provided information, Sample size (n) = 14 Level of significance (α) = 0.05

Answered: Scientists and engineers frequently…

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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Scientists and engineers frequently wish to compare two different techniques for measuring or determining the value of a variable. In such situations, interest centers on testing whether the mean difference in measurements is zero. An article reports the accompanying data on amount of milk ingested by each of 14 randomly selected infants.

	Infant
1	2	3	4	5	6	7	8	9	10	11	12	13	14
DD method	1509	1418	1561	1556	2169	1740	1098	1198	1479	1281	1414	1934	2174	2058
TW method	1498	1254	1326	1565	2000	1318	1410	1129	1342	1144	1468	1604	1722	1528
Difference	11	164	235	−9	169	422	−312	69	137	137	−54	330	452	530

Does it appear that the true average difference between intake values measured by the two methods is something other than zero? Determine the P-value of the test, and use it to reach a conclusion at significance level 0.05. Calculate the test statistic and P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.)

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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