Answered: Find the test statistic, critical…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.1: Real Numbers

Problem 30E

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Nine experts rated two brands of coffee in a taste-testing experiment. A rating on a 7-point scale (1=extremely unpleasing, 7=extremely pleasing) is given for each of four characteristics: taste, aroma, richness, and acidity. The accompanying data table contains the ratings accumulated over all four characteristics.

Find the test statistic, critical vlaues, p-value and construct a 95% confidence interval estimate of the difference in the mean ratings between the two brands.

Transcribed Image Text:Expert C. Brand A Brand B 24 26 S.E. 26 26 E.G 18 19 B.I. 21 23 C.M. C.N. 21 23 24 25 G.N. 25 24 R.M. 24 26 P.V. 22 24

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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