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:

Plasma

The liquid component of blood, without cells, consisting mainly of water, proteins, salts, lipids, and glucose, which serves as a medium for transporting nutrients, hormones, and waste products.

Blood Volume

The total amount of blood circulating within an individual's vascular system.

Proerythroblasts

Immature red blood cell precursors found in the bone marrow, which eventually mature into erythrocytes.

Red Blood Cells

A rephrased definition of erythrocytes; these are cells in the bloodstream that carry oxygen from the lungs to the rest of the body and return carbon dioxide for exhalation.