An agronomist would like to estimate the average weight of all Indian River County grapefruits. The mean weight of a random sample of 262 Indian River County grapefruits was found to be 203 grams. The standard deviation of the weights of all Indian River County grapefruit is known to be 20 grams. Find three different confidence intervals - one with a 97% confidence level, one with a 95% confidence level, and one with a 90% confidence level - for the mean weight of all Indian River County grapefruits. Notice how the confidence level affects the margin of error and the width of the interval. Report confidence interval solutions using interval notation. Round solutions to two decimal places, if necessary. The margin of error for a 97% confidence interval is given by E=E=. A 97% confidence interval is given by . The margin of error for a 95% confidence interval is given by E=E=. A 95% confidence interval is given by . The margin of error for a 90% confidence interval is given by E=E=. A 90% confidence interval is given by . If the level of confidence is decreased, leaving all other characteristics constant, the margin of error of the confidence interval will . If the level of confidence is decreased, leaving all other characteristics constant, the width of the confidence interval will .

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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An agronomist would like to estimate the average weight of all Indian River County grapefruits. The mean weight of a random sample of 262 Indian River County grapefruits was found to be 203 grams. The standard deviation of the weights of all Indian River County grapefruit is known to be 20 grams.

Find three different confidence intervals - one with a 97% confidence level, one with a 95% confidence level, and one with a 90% confidence level - for the mean weight of all Indian River County grapefruits. Notice how the confidence level affects the margin of error and the width of the interval.

Report confidence interval solutions using interval notation. Round solutions to two decimal places, if necessary.

The margin of error for a 97% confidence interval is given by E=E=.

A 97% confidence interval is given by .
The margin of error for a 95% confidence interval is given by E=E=.

A 95% confidence interval is given by .
The margin of error for a 90% confidence interval is given by E=E=.

A 90% confidence interval is given by .

If the level of confidence is decreased, leaving all other characteristics constant, the margin of error of the confidence interval will .

If the level of confidence is decreased, leaving all other characteristics constant, the width of the confidence interval will .

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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