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

question 29

Essay

Assume that under the null hypothesis, $\bar { Y }$ 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 p-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.,, ${ } ^ { \mu } \gamma$ = 540, 530, 520, etc.?

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Definitions:

Cost Of Goods Sold

The direct costs attributable to the production of the goods sold in a company, including materials and labor.

Gross Profit

The profit a company makes after deducting the costs associated with making and selling its products, or the costs associated with providing its services.

Single-Step

A simplified method used in income statement preparation that aggregates all revenues and subtracts all expenses to calculate net income.

Multiple-Step

A detailed income statement format that separates operational revenue and expenses from non-operational ones to highlight core business profitability.