The Following Data for Five Years of the Annual Returns

question 107

Multiple Choice

The following data for five years of the annual returns for two of Vanguard's mutual funds, the Vanguard Energy Fund (x) and the Vanguard Healthcare Fund (y) , were given as s_x = 35.77, s_y = 13.34, s_xy = 447.68. The competing hypotheses are H₀: ρ_xy = 0, H_A: ρ_xy ≠ 0. At the 5% significance level which of the following is the correct conclusion to the test?

• A) Reject the null hypothesis; we can conclude that the returns of these two mutual funds are correlated.
• B) Reject the null hypothesis; we cannot conclude that the returns of these two mutual funds are not correlated.
• C) Do not reject the null hypothesis; we can conclude that the returns of these two mutual funds are correlated.
• D) Do not reject the null hypothesis; we cannot conclude that the returns of these two mutual funds are correlated

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Definitions:

Glands

Organs in the body that synthesize substances such as hormones or sweat, secreting them for use throughout the body or excreting them for removal.

Allostatic Load

The wear and tear on the body accumulated through chronic stress, significantly impacting physical and mental health.

Physiological Stress

A reaction of the body to a stimulus or environment that disturbs the physical or mental equilibrium, causing strain to the body's systems.

Central Nervous System

A complex system of nerves and cells that control activities within the body, comprising the brain and spinal cord.