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Name: Heights were measured for a random sample of 21 plants grown while bei
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Description: Heights were measured for a random sample of 21 plants grown while being treated with a particular nutrient. The sample mean and sample standard deviation of those height measurements were 38 centimeters and 7 centimeters, respectively. Assume that t

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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Heights were measured for a random sample of 21 plants grown while being treated with a particular nutrient. The sample mean and sample standard deviation of those height measurements were 38 centimeters and 7 centimeters, respectively. Assume that the population of heights of treated plants is normally distributed with mean μ. Based on the sample, can it be concluded that μ is different from 42 centimeters? Use the 0.05 level of significance.

State the null hypothesis H0and the alternative hypothesis H1
Using the t-test find the value
Find two critical value
At the 0.05 level of significance, can it be concluded that the population mean height of treated plants is different from 42 centimeters? Yes or No?

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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