Chicken diet and weight: Compare the effects of six types of feed: casein, horsebean, linseed, meat meal, soybean, and sunflower. The ANOVA output below can be used to test for differences between the mean weights of chicks on different diets. df Sum Sq Mean Sq F value Pr(>F) feed 5 231129.16 46225.83 15.36 0.0000 residuals 65 195556.02 3008.55 If we conducted a hypothesis test to determine if these data provide convincing evidence that the mean weight of chicks varies across some (or all) groups we would find a difference between mean weight of chicks between at least two of the diets using an overall αα = 0.05. Mean SD n casein 323.58 64.43 12 horsebean 160.2 38.63 10 linseed 218.75 52.24 12 meatmeal 276.91 64.9 11 soybean 246.43 54.13 14 sunflower 328.92 48.84 12 Now use the summary above to test that casein and horsebean have a different effect on mean weights of chicks. Find the alpha level to use for this pairwise comparison to four decimal places: α=α= Fcdf = (Round to three decimal places.) The test statistic for this pairwise comparison is: t = (Round to three decimal places.) The p-value = (Round to three decimal places.) Interpret the result of the pairwise comparison in the context of the study: There is enough evidence to show that casein and horsebean feeds have a different effect on the mean weights of chicks There is not enough evidence to show that casein and horsebean feeds have a different effect on the mean weights of chicks

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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Chicken diet and weight: Compare the effects of six types of feed: casein, horsebean, linseed, meat meal, soybean, and sunflower. The ANOVA output below can be used to test for differences between the mean weights of chicks on different diets.

	df	Sum Sq	Mean Sq	F value	Pr(>F)
feed	5	231129.16	46225.83	15.36	0.0000
residuals	65	195556.02	3008.55

If we conducted a hypothesis test to determine if these data provide convincing evidence that the mean weight of chicks varies across some (or all) groups we would find a difference between mean weight of chicks between at least two of the diets using an overall αα = 0.05.

	Mean	SD	n
casein	323.58	64.43	12
horsebean	160.2	38.63	10
linseed	218.75	52.24	12
meatmeal	276.91	64.9	11
soybean	246.43	54.13	14
sunflower	328.92	48.84	12

Now use the summary above to test that casein and horsebean have a different effect on mean weights of chicks.
Find the alpha level to use for this pairwise comparison to four decimal places: α=α=
Fcdf = (Round to three decimal places.)
The test statistic for this pairwise comparison is: t = (Round to three decimal places.)
The p-value = (Round to three decimal places.)

Interpret the result of the pairwise comparison in the context of the study:

There is enough evidence to show that casein and horsebean feeds have a different effect on the mean weights of chicks
There is not enough evidence to show that casein and horsebean feeds have a different effect on the mean weights of chicks

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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