Concussions and Brain Size A recent study1 examined the relationship of football and concussions on hippocampus volume in the brain. The study included three groups with in each group: healthy controls who had never played football, football players with no history of concussions, and football players with a history of concussions. In this exercise, we test for evidence that average brain size is larger in football players who have never had a concussion (FBNoConcuss) than in football players with a history of concussions (FBConcuss). The data are in FootballBrain where the variable Hipp measures brain size as the volume of the hippocampus (in ml) for each subject. Let group be the football players with no concussion and group be the football players with a history of concussions.

Part A: Null hypothesis. H₀: M₁ = M₂

Alternative hypothesis, H₁ : M₁ > M₂

Part B: x1-x2 = 6459-5735 = 724

Part C: p-value = 0.000

Part D: No, the difference in brain size is not due to random chance

Explanation:

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$527.7.if the following was the question  $527.7 is the answer.students who are trying to raise funds have an agreement with a local pizza chain. the chain has agreed to sell them pizzas at a discount, which the students can then resell to families in the local community for a profit. it is expected that of the 500 families in the community, at most 70% will buy pizza. based on a survey of their personal preferences, the students believe that they should order no more than 120 cheese pizzas, no more than 150 pepperoni pizzas, and no more than 100 vegetarian pizzas. they also want to make sure that at least 20% of the total pizzas are cheese and at least 50% of the pizzas are pepperoni. they make a profit of $1.45, $1.75, and $1.98, respectively, for each cheese, pepperoni, and vegetarian pizza they resell. how many pizzas of each type should they buy?