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
Bullish: 409 Neutral: 299 Bearish: 291
Develop a point estimate of the following population parameters (to 2 decimals).
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.
The total number = 409 + 299 + 291 = 999
A) 409/999 = 0.4094 or 0.41
B) 299/999 = 0.2993 or 0.30
C) 291/999 = 0.2913 or = 0.29
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To develop point estimates for the population parameters, you need to calculate the proportions based on the sample results provided.
a. To find the point estimate for the proportion of AAII subscribers who are bullish on the stock market, divide the number of bullish subscribers by the total number of respondents:
Point Estimate = Number of Bullish / Total Respondents
Point Estimate = 409 / (409 + 299 + 291)
b. To find the point estimate for the proportion of AAII subscribers who are neutral on the stock market, divide the number of neutral subscribers by the total number of respondents:
Point Estimate = Number of Neutral / Total Respondents
Point Estimate = 299 / (409 + 299 + 291)
c. To find the point estimate for the proportion of AAII subscribers who are bearish on the stock market, divide the number of bearish subscribers by the total number of respondents:
Point Estimate = Number of Bearish / Total Respondents
Point Estimate = 291 / (409 + 299 + 291)
Now, let's calculate the point estimates for each population parameter:
a. Point Estimate for bullish subscribers:
Point Estimate = 409 / (409 + 299 + 291) = 0.40 (or 40%)
b. Point Estimate for neutral subscribers:
Point Estimate = 299 / (409 + 299 + 291) = 0.29 (or 29%)
c. Point Estimate for bearish subscribers:
Point Estimate = 291 / (409 + 299 + 291) = 0.28 (or 28%)
Therefore, the point estimates for each population parameter are as follows:
a. Proportion of bullish subscribers: 0.40 (or 40%)
b. Proportion of neutral subscribers: 0.29 (or 29%)
c. Proportion of bearish subscribers: 0.28 (or 28%)