Answered: A study was conducted in which two…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

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A study was conducted in which two types of engines, X and Y, were compared. Gas mileage, in miles per gallon, was measured. Fifty experiments were conducted using engine type X and 75 experiments were done with engine type Y. The gasoline used and other conditions were held constant. The average gas mileage was 36 miles per gallon for engine X and 42 miles per gallon for engine Y. Find a 96% confidence interval on μY − μX, where μX and μY are population mean gas mileages for engines X and Y, respectively. Assume that the population standard deviations are 6 and 8 for engines X and Y, respectively.

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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how do you get 2.0537? step-by-step process, please.

Confidence interval
From z tables, P (z~2.0537) = 0.02
20.04 = 2.0537
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