The Sample Mean and the Sample Standard Deviation of Annual

question 115

Essay

The sample mean and the sample standard deviation of annual returns on a stock over a 12-year period as computed by a stock analyst were 18% and 12%, respectively. The analyst wants to know if the risk, as measured by the standard deviation, differs from 15%.
A) Construct a 90% confidence interval of the population variance and the population standard deviation.
B) What assumption is required in constructing the confidence interval?
C) Based on the above confidence interval, does the risk differ from 15%?

• A) Construct a 90% confidence interval of the population variance and the population standard deviation.
• B) What assumption is required in constructing the confidence interval?
• C) Based on the above confidence interval, does the risk differ from 15%?

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Definitions:

Operational Definition

A clear, detailed description of a process, concept, or variable in terms of the procedures or operations required to measure it.

Depression

A mental health disorder characterized by persistently depressed mood or loss of interest in activities, affecting daily functioning.

Conscientiousness

A personality trait characterized by being thorough, careful, or vigilant; entails a strong sense of duty and being responsible.

Determinism

The philosophical concept that every event or state of affairs, including every human decision and action, is the consequence of preceding events in accordance with the natural laws.