Visualizing Statistical PrecisionEach graph below shows a scatter plot of an outcome (y or w) over x. The red circles represent the sample means of the two groups. Both graphs have 50 observations in the 0-group and 50 observations in the 1-group and the axes on both graphs are identical. The difference between group averages is also the same (group-1 average is 37 higher than group-0). Below are the results of t-tests for the difference in means for each outcome. The results are in no particular order.Results 1 group-1 meangroup-0 meandifferencestandard errort-statp-value 182145375.76.49<0.001 Results 2 group-1 meangroup-0 meandifferencestandard errort-statp-value 1821453712.13.060.003 Which results correspond to the difference in means for outcome y?a. Results 1b. Results 2c. Not enough information to determine XBelow are the results of t-tests for the difference in means for each outcome. The results are in noparticular order.Results 1group-1 group-0standarddifferencet-statp-valuemeanmeanerror182145375.76.49<0.001Results 2group-1 group-0standarddifferencet-statp-valuemeanmeanerror1821453712.13.060.003150 200 250 300 350001 09300 350

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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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Visualizing Statistical Precision

Each graph below shows a scatter plot of an outcome (y or w) over x. The red circles represent the sample means of the two groups. Both graphs have 50 observations in the 0-group and 50 observations in the 1-group and the axes on both graphs are identical. The difference between group averages is also the same (group-1 average is 37 higher than group-0).

Below are the results of t-tests for the difference in means for each outcome. The results are in no particular order.

Results 1	group-1 mean	group-0 mean	difference	standard error	t-stat	p-value
	182	145	37	5.7	6.49	<0.001

Results 2	group-1 mean	group-0 mean	difference	standard error	t-stat	p-value
	182	145	37	12.1	3.06	0.003

Which results correspond to the difference in means for outcome y?

a. Results 1

b. Results 2

c. Not enough information to determine

X
Below are the results of t-tests for the difference in means for each outcome. The results are in no
particular order.
Results 1
group-1 group-0
standard
difference
t-stat
p-value
mean
mean
error
182
145
37
5.7
6.49
<0.001
Results 2
group-1 group-0
standard
difference
t-stat
p-value
mean
mean
error
182
145
37
12.1
3.06
0.003
150 200 250 300 350
001 09
300 350

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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