An investigation was carried out to study possible consequences of the high incidence of head injuries among soccer players. Three groups of college students (soccer athletes, nonsoccer athletes, and a control group consisting of students who did not participate in intercollegiate sports) were considered in the study. The following table gives information on scores from the Hopkins Verbal Learning Test (which measures immediate memory recall). In addition = 30.0391. Soccer Athletes Nonsoccer Athletes Control Sample size 87 96 52 Sample mean score 30.90 29.54 29.52 Sample standard deviation 3.93 5.34 3.98 Suppose that it is reasonable to regard these three samples as random samples from the three student populations of interest. Is there sufficient evidence to conclude that the means for Hopkins score are not the same for the three student populations? Use ? = 0.05. (Round your answer to two decimal places.) F = Use technology to find the P-value. (Round your answer to four decimal places.) P-value = What can you conclude? Reject H0. The data provide convincing evidence that the means for Hopkins score are not the same for the three student populations.Fail to reject H0. The data provide convincing evidence the means for Hopkins score are not the same for the three student populations. Fail to reject H0. The data do not provide convincing evidence that the means for Hopkins score are not the same for the three student populations.Reject H0. The data do not provide convincing evidence that the means for Hopkins score are not the same for the three student populations.

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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An investigation was carried out to study possible consequences of the high incidence of head injuries among soccer players. Three groups of college students (soccer athletes, nonsoccer athletes, and a control group consisting of students who did not participate in intercollegiate sports) were considered in the study. The following table gives information on scores from the Hopkins Verbal Learning Test (which measures immediate memory recall). In addition = 30.0391.

	Soccer Athletes	Nonsoccer Athletes	Control
Sample size	87	96	52
Sample mean score	30.90	29.54	29.52
Sample standard deviation	3.93	5.34	3.98

Suppose that it is reasonable to regard these three samples as random samples from the three student populations of interest.

Is there sufficient evidence to conclude that the means for Hopkins score are not the same for the three student populations? Use

? = 0.05.

(Round your answer to two decimal places.)

F =

Use technology to find the P-value. (Round your answer to four decimal places.)

P-value =

What can you conclude?

Reject H₀. The data provide convincing evidence that the means for Hopkins score are not the same for the three student populations.Fail to reject H₀. The data provide convincing evidence the means for Hopkins score are not the same for the three student populations. Fail to reject H₀. The data do not provide convincing evidence that the means for Hopkins score are not the same for the three student populations.Reject H₀. The data do not provide convincing evidence that the means for Hopkins score are not the same for the three student populations.

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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