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Description: From previous experience, the owner of an apple orchard knows that the mean weight of Gala apples is 140 grams. There has been more precipitation than usual this year, and the owner believes the weights of the apples will be heavier than usual. The o

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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From previous experience, the owner of an apple orchard knows that the mean weight of Gala apples is 140 grams. There has been more precipitation than usual this year, and the owner believes the weights of the apples will be heavier than usual. The owner takes a random sample of 30 apples and records their weights. The mean weight of the sample is 144 grams with a standard deviation of 13.2 grams. A significance test at an alpha level of produces a P-value of 0.054. What is the correct interpretation of the P-value?

There is a 5.4% chance that the null hypothesis is incorrect if the true mean weight is 140 grams.

There is a 5.4% chance that a sample mean of 144 grams or greater will occur by chance if the true mean weight is 140 grams.

There is a 5.4% probability that a sample mean of 144 grams will occur by chance alone if the true mean weight is 140 grams.

Assuming the true mean weight of the apples is 140 grams, there is a 94.6% probability that a random sample of apples will produce a mean weight of 140 grams.

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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