Researchers sampled fish from a lake and measured the lengths (mm) of all individuals of two species, bream and perch. They were interested in testing whether there was a difference in the mean lengths of the two species in the lake. Based on the output below, what would be the correct conclusion to draw? MeannStd deviationStd error of meanBream531.006309.60126.39Perch154.821178.7623.75 options: Bream are significantly larger on average than perch in this lake. There is no significant difference in average sizes of the two species of fish from this lake. The variances are different so it is not possible to do a statistical test comparing means. Perch are significantly larger on average than bream in this lake. length 11000008600400200BreamspeciesPerchTwo Sample t-testdata: length1 by speciest = 3.9019, df = 15, p-value = 0.001416alternative hypothesis: true difference in means is not equal to 0.95 percent confidence interval:170.6882 581.6755sample estimates:mean in group Bream mean in group Perch531.0000154.8182Welch Two Sample t-testdata: lengthi by speciest = 2.9251, df = 5.356, p-value = 0.03024alternative hypothesis: true difference in means is not equal to 095 percent confidence interval:52.08779 700.27584sample estimates:mean in group Bream mean in group Perch531.0000154.8182

Let us consider two samples taken randomly Here, the two samples are independent of each other.…

Answered: esearchers sampled fish from a lake and…

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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Researchers sampled fish from a lake and measured the lengths (mm) of all individuals of two species, bream and perch. They were interested in testing whether there was a difference in the mean lengths of the two species in the lake. Based on the output below, what would be the correct conclusion to draw?

	Mean	n	Std deviation	Std error of mean
Bream	531.00	6	309.60	126.39
Perch	154.82	11	78.76	23.75

options:

	Bream are significantly larger on average than perch in this lake.
	There is no significant difference in average sizes of the two species of fish from this lake.
	The variances are different so it is not possible to do a statistical test comparing means.
	Perch are significantly larger on average than bream in this lake.

length 1
1000
008
600
400
200
Bream
species
Perch
Two Sample t-test
data: length1 by species
t = 3.9019, df = 15, p-value = 0.001416
alternative hypothesis: true difference in means is not equal to 0.
95 percent confidence interval:
170.6882 581.6755
sample estimates:
mean in group Bream mean in group Perch
531.0000
154.8182
Welch Two Sample t-test
data: lengthi by species
t = 2.9251, df = 5.356, p-value = 0.03024
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
52.08779 700.27584
sample estimates:
mean in group Bream mean in group Perch
531.0000
154.8182

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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