5. Downs and Abwender (2002) evaluated soccer players and swimmers to determine whether routi blows to the head experienced by soccer players produced long term neurological deficits. In the stuc neurological tests were administered to mature soccer players and swimmers. In a similar study. researcher obtained the following data: Soccer players N2 = 5 X2 = 6 SS2 = 24 Swimmers N1 = 8 X1 = 9 SS = %3D = 44 (a) Compute a 95% confidence interval for u1 - µ2, the population mean difference in neurologi-

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Please make sure with Ho that you set it equal to something, not anything else. 

**Study Analysis: Neurological Deficits in Soccer Players and Swimmers**

In their 2002 study, Downs and Abwender evaluated the impact of routine head blows experienced by soccer players on long-term neurological health. They compared these effects with swimmers who were less likely to experience such head impacts. The study administered neurological tests to mature soccer players and swimmers, resulting in the following data:

**Data Summary:**

- **Swimmers**
  - Sample size (\(N_1\)) = 8
  - Mean score (\(X_1\)) = 9
  - Sum of squares (\(SS_1\)) = 44

- **Soccer Players**
  - Sample size (\(N_2\)) = 5
  - Mean score (\(X_2\)) = 6
  - Sum of squares (\(SS_2\)) = 24

**Tasks:**

(a) **95% Confidence Interval Calculation**  
Compute the 95% confidence interval for \(\mu_1 - \mu_2\), representing the population mean difference in neurological scores between these two groups.

(b) **Effect Size Calculation**  
Determine an appropriate effect size, such as Cohen's \(d\), to quantify the mean neurological score difference between the groups.

(c) **Hypothesis Test**  
Conduct a hypothesis test to ascertain if the population mean neurological score for swimmers significantly differs from that of soccer players.
Transcribed Image Text:**Study Analysis: Neurological Deficits in Soccer Players and Swimmers** In their 2002 study, Downs and Abwender evaluated the impact of routine head blows experienced by soccer players on long-term neurological health. They compared these effects with swimmers who were less likely to experience such head impacts. The study administered neurological tests to mature soccer players and swimmers, resulting in the following data: **Data Summary:** - **Swimmers** - Sample size (\(N_1\)) = 8 - Mean score (\(X_1\)) = 9 - Sum of squares (\(SS_1\)) = 44 - **Soccer Players** - Sample size (\(N_2\)) = 5 - Mean score (\(X_2\)) = 6 - Sum of squares (\(SS_2\)) = 24 **Tasks:** (a) **95% Confidence Interval Calculation** Compute the 95% confidence interval for \(\mu_1 - \mu_2\), representing the population mean difference in neurological scores between these two groups. (b) **Effect Size Calculation** Determine an appropriate effect size, such as Cohen's \(d\), to quantify the mean neurological score difference between the groups. (c) **Hypothesis Test** Conduct a hypothesis test to ascertain if the population mean neurological score for swimmers significantly differs from that of soccer players.
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