Solve the Problem. -Three Randomly Selected Households Are Surveyed as a Pilot Project

question 29

Essay

Solve the problem.
-Three randomly selected households are surveyed as a pilot project for a larger survey to be conducted later.
The numbers of people in the households are 1, 4, and 8. Consider the values of 1, 4, and 8 to be a population.
Assume that samples of size n = 2 are randomly selected with replacement from the population of 1, 4, and 8.
The nine different samples are as follows: (1, 1), (1, 4), (1, 8), (4, 1), (4, 4), (4, 8), (8, 1), (8, 4), and (8, 8). (i) Find
the standard deviation of each of the nine samples, then summarize the sampling distribution of the standard
deviations in the format of a table representing the probability distribution. (ii) Compare the population
standard deviation to the mean of the sample standard deviations. (iii) Do the sample standard deviations
target the value of the population standard deviation? In general, do standard deviations make good estimators
of population standard deviation? Why or why not?

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Definitions:

Systematic Risk

The potential for loss inherent in the entire market or an entire market segment, also known as market risk or non-diversifiable risk.

Beta

A measure of a stock's volatility in relation to the overall market, indicating its risk level compared to the market average.

Capital Asset Pricing Model

An approach outlining the connection between inherent risks and the expected return of assets, with a focus on stocks.

SML

The Security Market Line, a graphical representation used in the capital asset pricing model (CAPM) to show the relationship between the risk of an investment and its expected return.