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:

Local Reflex

A simple, automatic response to a stimulus that occurs within a specific area of the body, without involvement of the brain.

Motility

The capability of cells, organisms, or substances to move actively and spontaneously, often as part of physiological processes.

Digestive Tract

A series of hollow organs joined in a long, twisting tube from the mouth to the anus, where food is broken down and nutrients absorbed.

Vagus Nerve

The tenth cranial nerve, which is a long and complex nerve extending from the brainstem to the abdomen, involved in controlling the heart, lungs, and digestive tract, as well as mediating visceral reflexes and sensations.