Traditional Students (G1)Online Students (G2)mean2.972.95standard deviation0.340.35sample size3322significance level: 0.05degree of freedom: 53#1) Fix the errors seen in the image below. IX. T-Statistic CalculationThe computation of the t-statistic was held in four phases.First, the SS was extracted from the standard deviation (s) formula s =The SS for group 1 was computed as 3.6992 from the formula 0.34 =The SS for group 2 was computed as 2.5725 from the formula 0.35 =0.09466.Second, the pooled variance (s) of 0.1183 was obtained using the formula: s =3.6992+2.5725SS₁ + SS₂df₁+df₂= 0.1183.32+21Third, the estimated standard error for the mean differences (S(M1-M2)) of 0.09466 was0.1183 0.1183+3322computed using the formula: S(M1-M2) =t ==X. P-Value6.271753Fourth, the t-statistic of 0.2112 is obtained, as shown below:(M₁-M₂)-(H₁-H₂) 2.97-2.95-0S(M1-M2)0.09466==+ =n1 n20.020.09466SS= 0.2112.SS3221= √0.008962 =The p-value was obtained using the t-distribution tableThe samplesizes of the two groups were 33 and 22, and the degree of freedom was 53. To find the p-value, it is necessary to look at the row corresponding to 53 at a significance level of 0.05and two tails. The value of the critical test statistic is 2. The computed t-statistic, 0.2112,falls between 0 and 0.679 from the same row. The next step is to look at the alpha levelsat the top of the table with two tails, corresponding to 0 and 0.679. These alpha levels are1 and 0.5. Therefore, the p-value of the test, which is 0.75, will be between 1 and 0.5. Thep-value was confirmed using the TI-84 obtaining a similar p-value of 0.7994.

Given data as follows:Traditional students (G1)Traditional students (G2)Mean2.972.95Standard…

Answered: The computation of the t-statistic was…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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	Traditional Students (G1)	Online Students (G2)
mean	2.97	2.95
standard deviation	0.34	0.35
sample size	33	22

significance level: 0.05

degree of freedom: 53

#1) Fix the errors seen in the image below.

IX. T-Statistic Calculation
The computation of the t-statistic was held in four phases.
First, the SS was extracted from the standard deviation (s) formula s =
The SS for group 1 was computed as 3.6992 from the formula 0.34 =
The SS for group 2 was computed as 2.5725 from the formula 0.35 =
0.09466.
Second, the pooled variance (s) of 0.1183 was obtained using the formula: s =
3.6992+2.5725
SS₁ + SS₂
df₁+df₂
= 0.1183.
32+21
Third, the estimated standard error for the mean differences (S(M1-M2)) of 0.09466 was
0.1183 0.1183
+
33
22
computed using the formula: S(M1-M2) =
t =
=
X. P-Value
6.2717
53
Fourth, the t-statistic of 0.2112 is obtained, as shown below:
(M₁-M₂)-(H₁-H₂) 2.97-2.95-0
S(M1-M2)
0.09466
=
=
+ =
n1 n2
0.02
0.09466
SS
= 0.2112.
SS
32
21
= √0.008962 =
The p-value was obtained using the t-distribution table
The sample
sizes of the two groups were 33 and 22, and the degree of freedom was 53. To find the p-
value, it is necessary to look at the row corresponding to 53 at a significance level of 0.05
and two tails. The value of the critical test statistic is 2. The computed t-statistic, 0.2112,
falls between 0 and 0.679 from the same row. The next step is to look at the alpha levels
at the top of the table with two tails, corresponding to 0 and 0.679. These alpha levels are
1 and 0.5. Therefore, the p-value of the test, which is 0.75, will be between 1 and 0.5. The
p-value was confirmed using the TI-84 obtaining a similar p-value of 0.7994.

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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