Answered: Jonathan Kent tests a new type of…

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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Question

Jonathan Kent tests a new type of chicken feed on 9 chickens. Their average weight is 64.38 ounces, with a standard deviation of 2.065 ounces. He finds a 95% confidence interval for the mean weight of all chickens which could be given the new feed is (62.79, 65.97) ounces.

Which of the following is a correct interpretation of the confidence interval?

95% of chickens would show mean weight between 62.79 and 65.97 ounces.

Either the mean chicken weight is between 62.79 and 65.97 ounces, or else our sample is among the 5% most unusual that could have been obtained.

95% of all chicken weights average between 62.79 and 65.97 ounces.

Chicken weights are between 62.79 and 65.97 ounces 95% of the time.

95% of the chickens sampled had weights between 62.79 and 65.97 ounces.

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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