Answered: Data on alcohol content and wine…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 91E

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Question

Data on alcohol content and wine quality was collected from variants of a particular wine. From a sample of 50 wines, a model was created using the percentages of alcohol to predict wine quality. The data are modeled by Yi=−0.384+0.5332Xi, where Xi is the alcohol content (%) and Yi is the rated quality of the wine. For these data, SYX=0.9431, X=10.19, and hi=0.029612 when X=11.

a. Construct a

90%

confidence interval estimate of the mean wine quality rating for all wines that have

11%

alcohol.

_____≤μY|X=11≤_______

(Type integers or decimals. Round to three decimal places as needed. Use ascending order.)

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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