A Decision Maker Wishes to Test the Following Null and Alternative

question 30

Multiple Choice

A decision maker wishes to test the following null and alternative hypotheses using an alpha level equal to 0.05: H₀ : μ₁ - μ₂ = 0
H_A : μ₁ - μ₂ ≠ 0
The population standard deviations are assumed to be known.After collecting the sample data,the test statistic is computed to be z = 1.78
Using the p-value approach,what decision should be reached about the null hypothesis?

• A)Since p-value = 0.0018 < α/2 = 0.025,reject the null hypothesis
• B)Since p-value = 0.0415 > α/2 = 0.025,do not reject the null hypothesis.
• C)Since p-value = 0.0033 < α/2 = 0.025,reject the null hypothesis.
• D)Since p-value = 0.0375 > α/2 = 0.025,do not reject the null hypothesis.

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Definitions:

Correlation Coefficient

A statistical measure that describes the extent to which two variables fluctuate together, ranging from -1 (perfect negative correlation) to +1 (perfect positive correlation).

Covariance

A measure of the degree to which two variables move in relation to each other, indicating the direction of their relationship.

Expected Return

The anticipated return on an investment, averaging in the probability of different outcomes.

Optimal Risky Portfolio

A portfolio construction that maximizes expected return for a given level of risk, based on modern portfolio theory.