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Description: In a study examining the effect of room temperature on academic performance, researchers tested knowledge of basic statistical concepts for two groups of Introduction to Statistics students who took their exams in rooms with different temperatures. O

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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In a study examining the effect of room temperature on academic performance, researchers tested knowledge of basic statistical concepts for two groups of Introduction to Statistics students who took their exams in rooms with different temperatures. One group took their exam in a room heated to 70 degrees Fahrenheit and the second group in a room heated to 90 degrees Fahrenheit.

With an alpha level of .05 and a two-tailed t test, the mean number of items students correctly answered in the 70 degree room (M = 7.9 out of 10, SD = 1.1) was significantly greater than the mean number of items students correctly answered in the 90 degree room (M = 6.6, SD = 1.3), t(22) = 2.44, p < .05, η² = .21.

1. Identify the independent and dependent variables for this study.

2. What is the significance level for this test? What does this value indicate?

3. What does t(22) indicate? How many participants are in this study?

4. What does 2.44 indicate?

5. What does p < .05 indicate?

6. What does η² = .21 indicate?

7. Can the researchers conclude that room temperature had a significant effect on academic performance? Explain.

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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