# The American Association of Individual Investors (AAII) polls its subscribers on a weekly basis...

## Question:

The American Association of Individual Investors (AAII) polls its subscribers on a weekly basis to determine the number who are bullish, bearish, or neutral on the short-term prospects for the stock market. Their findings for the week ending March 2, 2006, are consistent with the following sample results (AAII website, March 7, 2006). Bullish 409 Neutral 299 Bearish 291

Develop a point estimate of the following population parameters.

a. The proportion of all AAII subscribers who are bullish on the stock market.

b. The proportion of all AAII subscribers who are neutral on the stock market.

c. The proportion of all AAII subscribers who are bearish on the stock market.

d. What is the sampled population? What is the target population for parts (a), (b), and (c)? Would you be comfortable extending these results to the target population of all investors?

## Proportion

Proportion is the ratio of number of units belonging to a particul event A divided by total number of units in sample space that is the sample size n.The Proportion of unit of A is given by:

{eq}{p_A} = \dfrac{{n\left( A \right)}}{n} {/eq}

## Answer and Explanation:

Given Information:

Let the number of people in the sample taken from the American Association of Individual Investors (AAII) on weekly basis who are Bullish, Neutral and Bearish on the stock market be denoted by n(B),n(N) and n(Be) respectively.

{eq}\begin{align*} n\left( B \right) &= 409\\ n\left( N \right) &= 299\\ n\left( {Be} \right) &= 291 \end{align*} {/eq}

The total number of units in sample space is given by:

{eq}\begin{align*} n &= n\left( B \right) + n\left( N \right) + n\left( {Be} \right)\\ n &= 409 + 299 + 291\\ n &= 999 \end{align*} {/eq}

a. The proportion of all AAII subscribers who are bullish on the stock market is given by:

{eq}\begin{align*} {p_B} &= \dfrac{{n\left( B \right)}}{n}\\ &= \dfrac{{409}}{{999}}\\ &= 0.4094 \end{align*} {/eq}

The proportion of all AAII subscribers who are bullish on the stock market is 0.4094.

b. The proportion of all AAII subscribers who are neutral on the stock market is given by:

{eq}\begin{align*} {p_N} &= \dfrac{{n\left( N \right)}}{n}\\ &= \dfrac{{299}}{{999}}\\ &= 0.2993 \end{align*} {/eq}

The proportion of all AAII subscribers who are neutral on the stock market is 0.2993.

c. The proportion of all AAII subscribers who are bearish on the stock market is given by:

{eq}\begin{align*} {p_{Be}} &= \dfrac{{n\left( {Be} \right)}}{n}\\ &= \dfrac{{291}}{{999}}\\ &= 0.2913 \end{align*} {/eq}

The proportion of all AAII subscribers who are bearish on the stock market is 0.2913.

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from High School Algebra I: Help and Review

Chapter 23 / Lesson 15