Answered: Suppose samples of six different brands…

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

Suppose samples of six different brands of diet or imitation margarine were analyzed to determine the level of physiologically active polyunsaturated fatty acids (PAPUFA, in percent), resulting in the data shown in the accompanying table.

Imperial	14.1	13.6	14.6	14.3
Parkay	12.8	12.5	13.6	13.0	12.3
Blue Bonnet	13.5	13.4	14.1	14.5
Chiffon	13.2	12.7	12.6	14
Mazola	16.8	17.3	16.4	17.3	18.0
Fleischmann's	18.1	17.2	18.8	18.4

(a)

Test for differences among the true means for PAPUFA percentages among the different brands. Use

? = 0.05.

Calculate the test statistic. (Round your answer to two decimal places.)

F =

Use technology to find the P-value. (Round your answer to four decimal places.)

P-value =

What can you conclude?

Reject H₀. There is convincing evidence that the mean PAPUFA percentages for the six brands are not all equal.Fail to reject H₀. There is convincing evidence that the mean PAPUFA percentages for the six brands are not all equal. Reject H₀. There is not convincing evidence that the mean PAPUFA percentages for the six brands are not all equal.Fail to reject H₀. There is not convincing evidence that the mean PAPUFA percentages for the six brands are not all equal.

(b)

Use the T-K procedure to calculate 95% simultaneous confidence intervals for all differences between means. (Round your answers to three decimal places.)

Imperial and Parkay

Imperial and Blue Bonnet

Imperial and Chiffon

Imperial and Mazola

Imperial and Fleischmann's

Parkay and Blue Bonnet

Parkay and Chiffon

Parkay and Mazola

Parkay and Fleischmann's

Blue Bonnet and Chiffon

Blue Bonnet and Mazola

Blue Bonnet and Fleischmann's

Chiffon and Mazola

Chiffon and Fleischmann's

Mazola and Fleischmann's

Give the corresponding underscoring pattern.

	Parkay	Chiffon	Blue Bonnet	Imperial	Mazola	Fleischmann's
Sample Mean	12.84	13.125	13.875	14.15	17.16	18.125

	Parkay	Chiffon	Blue Bonnet	Imperial	Mazola	Fleischmann's
Sample Mean	12.84	13.125	13.875	14.15	17.16	18.125

	Parkay	Chiffon	Blue Bonnet	Imperial	Mazola	Fleischmann's
Sample Mean	12.84	13.125	13.875	14.15	17.16	18.125

	Parkay	Chiffon	Blue Bonnet	Imperial	Mazola	Fleischmann's
Sample Mean	12.84	13.125	13.875	14.15	17.16	18.125

	Parkay	Chiffon	Blue Bonnet	Imperial	Mazola	Fleischmann's
Sample Mean	12.84	13.125	13.875	14.15	17.16	18.125

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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