In Order to Test the Hypotheses:
H₀: µ $\mu$ ₁ - µ

question 47

Essay

In order to test the hypotheses:
H₀: µ $\mu$ ₁ - µ $\mu$ ₂ = 0
H₁: µ $\mu$ ₁ - µ $\mu$ ₂ ? $\neq$ 0,
we independently draw a random sample of 18 observations from a normal population with standard deviation of 15, and another random sample of 12 from a second normal population with standard deviation of 25.
a. If we set the level of significance at 5%, determine the power of the test when $\mu$ ₁ - $\mu$ ₂ = 5.
b. Describe the effect of reducing the level of significance on the power of the test.

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Definitions:

Demand Probability

The likelihood or chance that a product or service will be desired or required by the market at a certain time.

Monte Carlo Simulation

A statistical technique employing random variables to simulate a model numerous times, thereby estimating the probable outcomes of various decisions or future events.

Cumulative Probability

The probability that a random variable is less than or equal to a specific value, often visualized as the area under the probability distribution curve to that point.

Demand Probability

The likelihood that a product or service will be purchased at various price levels within a specified time period.