Two groups of students are tested after two types of instruction. Student Group 1 receives traditional instruction and Student Group 2 receives modified instruction. Below are the t-test results:t-Test: Two-Sample Assuming Equal Variances Students 1Students 2Mean15.316.9Variance4.92.766666667Observations1010Pooled Variance3.833333333 Hypothesized Mean Difference0 df18 t Stat-2.82732877 P(T<=t) one-tail0.042139087 t Critical one-tail1.734063607 P(T<=t) two-tail0.034278174 t Critical two-tail2.10092204 What is the null hypothesis? Use the two-tail probability. Is there a difference between the group of students in group 1 and students in group 2? In a few sentences, describe the results in terms of the statistics as you would for an academic article.

Let μ1 denotes the true average of group 1 and μ2 denotes the true average of group 2.

Answered: Two groups of students are tested after…

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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Two groups of students are tested after two types of instruction. Student Group 1 receives traditional instruction and Student Group 2 receives modified instruction. Below are the t-test results:

t-Test: Two-Sample Assuming Equal Variances

	Students 1	Students 2
Mean	15.3	16.9
Variance	4.9	2.766666667
Observations	10	10
Pooled Variance	3.833333333
Hypothesized Mean Difference	0
df	18
t Stat	-2.82732877
P(T<=t) one-tail	0.042139087
t Critical one-tail	1.734063607
P(T<=t) two-tail	0.034278174
t Critical two-tail	2.10092204

What is the null hypothesis?

Use the two-tail probability. Is there a difference between the group of students in group 1 and students in group 2?

In a few sentences, describe the results in terms of the statistics as you would for an academic article.

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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