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Name: A sample of 23 plants was taken and the mean height was 27 cm. A 95% c
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Description: A sample of 23 plants was taken and the mean height was 27 cm. A 95% confidence interval for the true mean height of plants of that particular species is (23.2 cm, 30.8 cm). Four students gave the following interpretations of the confidence interval.

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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A sample of 23 plants was taken and the mean height was 27 cm. A 95% confidence interval for the true mean height of plants of that particular species is (23.2 cm, 30.8 cm).

Four students gave the following interpretations of the confidence interval. Which of the following is correct?

1. We are 95% confident that the true mean height is 27 cm since that value lies in the confidence interval

2. We can be fairly confident that 95% of all plants of that species have a height between 23.2 cm and 30.8 cm.

3. The probability is 0.95 that the mean height lies in the interval (23.2 , 30.8).

4. We are 95% confident that the true mean height for all plants of that species will lie in the interval (23.2, 30.8)

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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