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Chapter 7: Problem 17

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 (http://www.aaii.com). 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.

Short Answer

Expert verified
The proportions are approximately: Bullish 0.409, Neutral 0.299, and Bearish 0.291.

Step by step solution

01

Understand What is Asked

We are asked to provide point estimates for the proportion of AAII subscribers who are bullish, neutral, or bearish. These estimates will give us an idea of the percentage of the population in each category.
02

Identify the Total Number of Respondents

The total number of respondents is the sum of bullish, neutral, and bearish subscribers. Thus, calculate: \[ 409 (\text{bullish}) + 299 (\text{neutral}) + 291 (\text{bearish}) = 999. \]
03

Calculate the Proportion of Bullish Respondents

The proportion of respondents who are bullish is given by the number of bullish respondents divided by the total number of respondents. Thus: \[ \text{Proportion bullish} = \frac{409}{999}. \]
04

Calculate the Proportion of Neutral Respondents

The proportion of respondents who are neutral is given by the number of neutral respondents divided by the total number of respondents. Thus: \[ \text{Proportion neutral} = \frac{299}{999}. \]
05

Calculate the Proportion of Bearish Respondents

The proportion of respondents who are bearish is given by the number of bearish respondents divided by the total number of respondents. Thus: \[ \text{Proportion bearish} = \frac{291}{999}. \]
06

Simplify or Calculate the Values

Convert the fractions to decimal form to provide the proportion estimates: - Bullish: \( \frac{409}{999} \approx 0.4094 \) - Neutral: \( \frac{299}{999} \approx 0.2993 \) - Bearish: \( \frac{291}{999} \approx 0.2913 \)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Proportion Calculation
Proportion calculation is all about determining how large a part of a whole is occupied by a specific category. In our example, calculating the proportion involves finding out the share of American Association of Individual Investors (AAII) subscribers falling into each sentiment category: bullish, neutral, or bearish.

Here鈥檚 how you break it down:
  • First, you need the total number of respondents, which is a sum of all categories. In this case, it's 999.
  • Next, for each category (bullish, neutral, bearish), divide the number of respondents in that category by the total number of respondents. This gives you the fraction.
  • Lastly, convert this fraction into a decimal to represent the proportion. For instance, the bullish proportion is calculated as \( \frac{409}{999} \) which approximates to 0.4094.
Understanding proportion is crucial in statistics as it helps you make sense of data in relative terms rather than absolute figures. This conversion into proportions or percentages can make interpreting survey results more intuitive.
Sample Survey
A sample survey is a technique used to gather data from only a portion of a larger population. In this scenario, AAII conducts a weekly survey to assess the market sentiment among its subscribers.

Sample surveys are advantageous because:
  • They are less resource-intensive compared to collecting data from the entire population.
  • They can often provide quick feedback or insights.
  • When done correctly, they offer a reliable snapshot of the larger group.
When conducting a sample survey, ensure that the sample represents the larger population adequately. This helps in making accurate inferences about the entire population. Random sampling methods and correct survey designs are crucial to achieve this representation.

The AAII survey is a typical example of using a sample to gain insights into the broader opinions among investors.
Statistical Analysis
Statistical analysis refers to the process of collecting, summarizing, and interpreting data to uncover patterns or trends. In this particular exercise, statistical analysis involves understanding how AAII subscribers view the market.

Key steps in statistical analysis:
  • **Collection**: Gathering the relevant data, as AAII does weekly.
  • **Summarization**: Using measures like proportion to convey the central tendency of respondent sentiments.
  • **Interpretation**: Deciphering what these summaries indicate about the entire subscriber sentiment on the stock market.
Through statistical analysis, AAII can potentially decide on strategic moves or advice based on prevailing subscriber sentiment.

The results from statistical analysis allow analyses, like determining whether a bullish sentiment correlates with stock market trends, or how market perceptions shift over time. This makes statistical analysis integral to making informed business and investment decisions.

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Most popular questions from this chapter

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