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Sample mean score 29.80 30.97 29.31 Sample standard deviation 3.72 5.19 3.79 In addition, = 30.17. 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 a = 0.05. State the appropriate null and alternative hypotheses. (Let 4, Hz. and uz be the true means for the three different groups.) O Ho ! My # Mz # Mg H, : at least two of the three u,'s are the same Ho: My = Hz = Hz H, : all three of the u's are different Ho : at least two of the three u,'s are different O Ho : all three of the u's are different O HoI My = H2 = Mg H: at least two of the three u's are different 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 reject Ho. The data provide convincing evidence that the mean Hopkins Verbal Learning Test score is not the same for the three student populations. O we fail to reject Hg. 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 Ho. The data do not provide convincing evidence that the mean Hopkins Verbal Learning Test score is not the same for the three student populations. O we fail to reject Ho. The data provide convincing evidence that the mean Hopkins Verbal Learning Test score is not the same for the three student populations.

Sample mean score 29.80 30.97 29.31 Sample standard deviation 3.72 5.19 3.79 In addition, = 30.17. 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 a = 0.05. State the appropriate null and alternative hypotheses. (Let 4, Hz. and uz be the true means for the three different groups.) O Ho ! My # Mz # Mg H, : at least two of the three u,'s are the same Ho: My = Hz = Hz H, : all three of the u's are different Ho : at least two of the three u,'s are different O Ho : all three of the u's are different O HoI My = H2 = Mg H: at least two of the three u's are different 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 reject Ho. The data provide convincing evidence that the mean Hopkins Verbal Learning Test score is not the same for the three student populations. O we fail to reject Hg. 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 Ho. The data do not provide convincing evidence that the mean Hopkins Verbal Learning Test score is not the same for the three student populations. O we fail to reject Ho. 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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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A study compared three groups of college students (soccer athletes, nonsoccer athletes, and a comparison group of non-athletes) to investigate the effects of head injuries on memory recall. The study assessed scores from the Hopkins Verbal Learning Test. The table below displays the sample size, mean scores, and standard deviations for each group: | Group | Soccer Athletes | Nonsoccer Athletes | Comparison Group | |-------------------------|-----------------|--------------------|------------------| | Sample size | 89 | 99 | 54 | | Sample mean score | 29.80 | 30.97 | 29.31 | | Sample standard deviation | 3.72 | 5.19 | 3.79 | The study posits that the samples are random from each group. The goal is to determine if there is sufficient evidence to conclude that the mean Hopkins score differs among the groups, using \(\alpha = 0.05\). **Hypotheses:** \( \mu_1, \mu_2, \mu_3 \) represent the true means for the groups. 1. \( H_0 \): All three means (\(\mu_1, \mu_2, \mu_3\)) are equal. \( H_a \): At least two of the three means are different. 2. \( H_0 \): At least two of the three means are equal. \( H_a \): All three means are different. Find the test statistic (F-value) and p-value using statistical software. Round the test statistic to two decimal places and the p-value to three decimal places: \( F = \_\_\_\_ \) \( p\text{-value} = \_\_\_\_ \) **Conclusion Options:** - Reject \( H_0 \): There is convincing evidence that the means are not the same across the three groups. - Fail to reject \( H_0 \): There is not convincing evidence that the means differ across the groups.
Transcribed Image Text:A study compared three groups of college students (soccer athletes, nonsoccer athletes, and a comparison group of non-athletes) to investigate the effects of head injuries on memory recall. The study assessed scores from the Hopkins Verbal Learning Test. The table below displays the sample size, mean scores, and standard deviations for each group: | Group | Soccer Athletes | Nonsoccer Athletes | Comparison Group | |-------------------------|-----------------|--------------------|------------------| | Sample size | 89 | 99 | 54 | | Sample mean score | 29.80 | 30.97 | 29.31 | | Sample standard deviation | 3.72 | 5.19 | 3.79 | The study posits that the samples are random from each group. The goal is to determine if there is sufficient evidence to conclude that the mean Hopkins score differs among the groups, using \(\alpha = 0.05\). **Hypotheses:** \( \mu_1, \mu_2, \mu_3 \) represent the true means for the groups. 1. \( H_0 \): All three means (\(\mu_1, \mu_2, \mu_3\)) are equal. \( H_a \): At least two of the three means are different. 2. \( H_0 \): At least two of the three means are equal. \( H_a \): All three means are different. Find the test statistic (F-value) and p-value using statistical software. Round the test statistic to two decimal places and the p-value to three decimal places: \( F = \_\_\_\_ \) \( p\text{-value} = \_\_\_\_ \) **Conclusion Options:** - Reject \( H_0 \): There is convincing evidence that the means are not the same across the three groups. - Fail to reject \( H_0 \): There is not convincing evidence that the means differ across the groups.
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