In a certain color test, 100 words that are color names are shown in colors different from the word. For example, the word red might be displayed in blue. The task is to correctly identify the display color of each word; in the example just given the correct response would be blue. Organizers recorded the time needed to complete this test for n = 16 individuals after they had consumed alcohol and for n = 16 other individuals after they had consumed a placebo drink flavored to taste as if it contained alcohol. Each group included eight men and eight women. In the alcohol group, the mean completion time was 135.25 seconds and the standard deviation was 22.64 seconds. In the placebo group, the mean completion time was 112.92 seconds and the standard deviation was 12.04 seconds. (a) Calculate the unpooled standard error for the difference in the two sample means. (Round your answer to four decimal places.) (b) Calculate a 95% confidence interval for the difference in population means. For the unpooled procedure, the approximate degrees of freedom are df = 22. (Round your answers to two decimal places.) to _ (c) On the basis of the confidence interval computed in part (b), can we conclude that the population means for the two groups are different? yes or no

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Description: In a certain color test, 100 words that are color names are shown in colors different from the word. For example, the word red might be displayed in blue. The task is to correctly identify the display color of each word; in the example just given the

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 certain color test, 100 words that are color names are shown in colors different from the word. For example, the word red might be displayed in blue. The task is to correctly identify the display color of each word; in the example just given the correct response would be blue. Organizers recorded the time needed to complete this test for n = 16 individuals after they had consumed alcohol and for n = 16 other individuals after they had consumed a placebo drink flavored to taste as if it contained alcohol. Each group included eight men and eight women. In the alcohol group, the mean completion time was 135.25 seconds and the standard deviation was 22.64 seconds. In the placebo group, the mean completion time was 112.92 seconds and the standard deviation was 12.04 seconds.

(a) Calculate the unpooled standard error for the difference in the two sample means. (Round your answer to four decimal places.)

(b) Calculate a 95% confidence interval for the difference in population means. For the unpooled procedure, the approximate degrees of freedom are df = 22. (Round your answers to two decimal places.)
__to ___

(c) On the basis of the confidence interval computed in part (b), can we conclude that the population means for the two groups are different?

yes or no

(d) Can we verify the necessary conditions for computing the confidence interval in part (b)?
determine whether the necessary conditions are present.

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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