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:

Eclectic Approach

A methodological approach that combines theories, principles, and strategies from multiple theoretical frameworks to address psychological issues.

Free Association

A psychoanalytic technique in which a patient says whatever comes to mind without filtering thoughts, aimed at uncovering unconscious thoughts and feelings.

Group Setting

A social context or environment where individuals gather together, often for a specific purpose or activity, influencing interactions and behavior within the group.

Drugs

Substances that alter the physiological or psychological state of an individual, which can include medications, narcotics, and psychoactive compounds.