A study compared three groups of college students (soccer athletes, nonsoccer athletes, and a comparison group consisting of students who did not participate in intercollegiate sports) to see if the high incidence of head injuries among soccer players might affect memory recall. The following is information on scores from the Hopkins Verbal Learning Test (which measures immediate memory recall). Group Soccer Athletes Nonsoccer Athletes Comparison Group Sample size 89 95 54 Sample mean score 29.90 30.99 29.38 Sample standard deviation 3.73 5.16 3.79 In addition, = 30.22. 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 mean Hopkins score is not the same for the three student populations? Use ? = 0.05. State the appropriate null and alternative hypotheses. (Let ?1, ?2, and ?3 be the true means for the three different groups.) H0 : at least two of the three ?i's are different Ha : ?1 = ?2 = ?3H0 : ?1 = ?2 = ?3 Ha : at least two of the three ?i's are different H0 : all three of the ?i's are different Ha : ?1 = ?2 = ?3H0 : ?1 = ?2 = ?3 Ha : all three of the ?i's are differentH0 : ?1 ≠ ?2 ≠ ?3 Ha : at least two of the three ?i's are the same Find the test statistic and P-value. (Use technology. Round your test statistic to two decimal places and your P-value to three decimal places.) F=P-value= State the conclusion in the problem context. We fail to reject H0. The data do not provide convincing evidence that the mean Hopkins Verbal Learning Test score is not the same for the three student populations.We reject H0. The data do not provide convincing evidence that the mean Hopkins Verbal Learning Test score is not the same for the three student populations. We fail to reject H0. The data provide convincing evidence that the mean Hopkins Verbal Learning Test score is not the same for the three student populations.We reject H0. The data provide convincing evidence that the mean Hopkins Verbal Learning Test score is not the same for the three student populations.

A study compared three groups of college students (soccer athletes, nonsoccer athletes, and a comparison group consisting of students who did not participate in intercollegiate sports) to see if the high incidence of head injuries among soccer players might affect memory recall. The following is information on scores from the Hopkins Verbal Learning Test (which measures immediate memory recall). Group Soccer Athletes Nonsoccer Athletes Comparison Group Sample size 89 95 54 Sample mean score 29.90 30.99 29.38 Sample standard deviation 3.73 5.16 3.79 In addition, = 30.22. 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 mean Hopkins score is not the same for the three student populations? Use ? = 0.05. State the appropriate null and alternative hypotheses. (Let ?1, ?2, and ?3 be the true means for the three different groups.) H0 : at least two of the three ?i's are different Ha : ?1 = ?2 = ?3H0 : ?1 = ?2 = ?3 Ha : at least two of the three ?i's are different H0 : all three of the ?i's are different Ha : ?1 = ?2 = ?3H0 : ?1 = ?2 = ?3 Ha : all three of the ?i's are differentH0 : ?1 ≠ ?2 ≠ ?3 Ha : at least two of the three ?i's are the same Find the test statistic and P-value. (Use technology. Round your test statistic to two decimal places and your P-value to three decimal places.) F=P-value= State the conclusion in the problem context. We fail to reject H0. The data do not provide convincing evidence that the mean Hopkins Verbal Learning Test score is not the same for the three student populations.We reject H0. The data do not provide convincing evidence that the mean Hopkins Verbal Learning Test score is not the same for the three student populations. We fail to reject H0. The data provide convincing evidence that the mean Hopkins Verbal Learning Test score is not the same for the three student populations.We reject H0. The data provide convincing evidence that the mean Hopkins Verbal Learning Test score is 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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Question

Group	Soccer Athletes	Nonsoccer Athletes	Comparison Group
Sample size	89	95	54
Sample mean score	29.90	30.99	29.38
Sample standard deviation	3.73	5.16	3.79

In addition,

= 30.22.

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 mean Hopkins score is not the same for the three student populations? Use

? = 0.05.

State the appropriate null and alternative hypotheses. (Let ?₁, ?₂, and ?₃ be the true means for the three different groups.)

H₀ : at least two of the three ?_i's are different
H_a : ?₁ = ?₂ = ?₃H₀ : ?₁ = ?₂ = ?₃
H_a : at least two of the three ?_i's are different H₀ : all three of the ?_i's are different
H_a : ?₁ = ?₂ = ?₃H₀ : ?₁ = ?₂ = ?₃
H_a : all three of the ?_i's are differentH₀ : ?₁ ≠ ?₂ ≠ ?₃
H_a : at least two of the three ?_i's are the same

Find the test statistic and P-value. (Use technology. Round your test statistic to two decimal places and your P-value to three decimal places.)

F=P-value=

State the conclusion in the problem context.

We fail to reject H₀. The data do not provide convincing evidence that the mean Hopkins Verbal Learning Test score is not the same for the three student populations.We reject H₀. The data do not provide convincing evidence that the mean Hopkins Verbal Learning Test score is not the same for the three student populations. We fail to reject H₀. The data provide convincing evidence that the mean Hopkins Verbal Learning Test score is not the same for the three student populations.We reject H₀. The data provide convincing evidence that the mean Hopkins Verbal Learning Test score is 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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