Math SAT Scores $( Y )$ Are Normally Distributed with a Mean of 500 and a a Mean

question 2

Essay

Math SAT scores $( Y )$ are normally distributed with a mean of 500 and a standard deviation of 100. An evening school advertises that it can improve students' scores by roughly a third of a standard deviation, or 30 points, if they attend a course which runs over several weeks. (A similar claim is made for attending a verbal SAT course.) The statistician for a consumer protection agency suspects that the courses are not effective. She views the situation as follows: $H _ { 0 } : \mu _ { Y } = 500$ vs. $H _ { 1 } : \mu _ { Y } = 530$ . (a)Sketch the two distributions under the null hypothesis and the alternative hypothesis.

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Definitions:

Nash Equilibrium

A concept in game theory where each player's strategy is optimal, given the strategies of other players, leading to a situation where no player has an incentive to deviate from their chosen strategy.

Marginal Cost

Marginal Cost is the increase in cost that arises from the production of one additional unit of a product or service.

Antitrust Laws

Antitrust laws are regulations designed to promote competition and prevent monopolies, ensuring fair practices in the marketplace.

Nash Equilibrium

A concept in game theory where each player's chosen strategy maximizes their payoff given the strategies chosen by other players, and no player can benefit by changing their strategy unilaterally.