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:

Policy

A deliberate system of principles to guide decisions and achieve rational outcomes, often enacted by a governmental or corporate entity.

Short Run

A period in economics during which at least one input, such as factory capacity, is fixed and cannot be changed.

Unemployment Benefits

Payments made by the government or a social insurance scheme to unemployed individuals who meet certain eligibility criteria.

Aggregate Demand

The combined demand for goods and services across an economy, pegged at a particular overall price level during a predetermined time period.