Stats Problem Set 11 Two-sample t-tests (independent samples) The local school district is comparing two methods for teaching mathematics to third-grade children. One class of n = 20 students is being taught by method A, and another class of n = 20 is being taught by method B. At the end of the school year, all of the students take a standardized math achievement test. The scores for the students taught by method A produced a mean of M = 75 with s2 = 95, and the students taught by method B had a mean of M = 87 with s2 = 105. It is expected that method A will yield better results on the achievement test. a.- What is the null hypothesis? b.- What is the research hypothesis? c.- Find the critical t value by using the table in Appendix B2 in your book. Remember that to find the total degrees of freedom, you will use the exact df, and if it is not in the table, round down to the nearest df. d.- Compute the estimated standard error for the test. Show all of your work. e.- Compute the t-value using a one-tailed test with α = .05. Show all of your work. f. Do you reject the null hypothesis or fail to reject it? Is method A better than method B? g. What is the size of the effect? Is this a small, medium, or large effect? Show all of your work. (Use the formula on page 208 in Chapter 11 and the guidelines for interpreting effect sizes on page 196 in Chapter 10). Both will be attached to this assignment.

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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Stats Problem Set 11

Two-sample t-tests (independent samples)

The local school district is comparing two methods for teaching mathematics to third-grade children. One class of n = 20 students is being taught by method A, and another class of n = 20 is being taught by method B. At the end of the school year, all of the students take a standardized math achievement test. The scores for the students taught by method A produced a mean of M = 75 with s2 = 95, and the students taught by method B had a mean of M = 87 with s2 = 105. It is expected that method A will yield better results on the achievement test.

a.- What is the null hypothesis?

b.- What is the research hypothesis?

c.- Find the critical t value by using the table in Appendix B2 in your book. Remember that to find the total degrees of freedom, you will use the exact df, and if it is not in the table, round down to the nearest df.

d.- Compute the estimated standard error for the test. Show all of your work.

e.- Compute the t-value using a one-tailed test with α = .05. Show all of your work.

f. Do you reject the null hypothesis or fail to reject it? Is method A better than method B?

g. What is the size of the effect? Is this a small, medium, or large effect? Show all of your work. (Use the formula on page 208 in Chapter 11 and the guidelines for interpreting effect sizes on page 196 in Chapter 10). Both will be attached to this assignment.

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Effect Size Formula
X₁ - X₂
ES =
of +0
2
• ES is the effect size
•
•
•
X₁ is the mean of group 1
X2 is the mean of group 2
o is the variance of group 1
6 is the variance of group 2
Guidelines for interpretating effect size
•
A small effect size range from 0 to .2
•
A medium effect size range from .2 to .8
•
A large effect size ranges is any value above .8.

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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