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Assume That Under the Null Hypothesis Yˉ\bar { Y } Has an Expected Value of 500 and a Standard Deviation

question 38

Essay

Assume that under the null hypothesis, Yˉ\bar { Y } has an expected value of 500 and a standard deviation of 20. Under the alternative hypothesis, the expected value is 550 . Sketch the probability density function for the null and the alternative hypothesis in the same figure. Pick a critical value such that the pp -value is approximately 5\%. Mark the areas, which show the size and the power of the test. What happens to the power of the test if the alternative hypothesis moves closer to the null hypothesis, i.e., μY=540,530,520\mu _ { Y } = 540,530,520 , etc.? 25

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Definitions:

Essential Nutrient

Nutrients that the body cannot synthesize on its own and must be obtained from the diet.

Calories

Units used to measure the amount of energy food provides to the body.

Essential Amino Acids

Amino acids that cannot be synthesized by the body and must be obtained from the diet, crucial for various bodily functions.

Proteins

Organic compounds made of amino acids, essential for the growth, repair, and maintenance of body tissues.

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