91Ó°ÊÓ

Do you think the government protects investors adequately? This question was part of an online survey of investors under age 65 living in the United States and Great Britain (Financial Times/Harris Poll, October 1,2009 ). The number of investors from the United States and the number of investors from Great Britain who answered Yes, No, or Unsure to this question are provided as follows. a. Estimate the probability that an investor living in the United States thinks the government is not protecting investors adequately. b. Estimate the probability that an investor living in Great Britain thinks the government is not protecting investors adequately or is unsure the government is protecting investors adequately. c. For a randomly selected investor from these two countries, estimate the probability that the investor thinks the government is not protecting investors adequately. d. Based upon the survey results, does there appear to be much difference between the perceptions of investors living in the United States and investors living in Great Britain regarding the issue of the government protecting investors adequately?

Step by step solution

01

Analyze Provided Data

We have results from two groups: United States (US) and Great Britain (GB). For the US: Yes = 48, No = 68, Unsure = 34; and for GB: Yes = 21, No = 43, Unsure = 36.

02

Calculate US 'No' Probability

The probability that a US investor answered 'No' is given by the formula: \( P_{US}(No) = \frac{\text{Number of 'No' in US}}{\text{Total responses in US}} = \frac{68}{48+68+34} = \frac{68}{150} \approx 0.4533 \).

03

Calculate GB 'No or Unsure' Probability

The probability that a GB investor answered either 'No' or 'Unsure' is: \( P_{GB}(No \, or \, Unsure) = \frac{\text{Number of 'No' in GB} + \text{Number of 'Unsure' in GB}}{\text{Total GB responses}} = \frac{43+36}{21+43+36} = \frac{79}{100} = 0.79 \).

04

Calculate Combined 'No' Probability

To find the overall probability that an investor from either country thinks the government is not protecting adequately, sum the 'No' responses and the total responses: \( P_{combined}(No) = \frac{68 + 43}{150 + 100} = \frac{111}{250} = 0.444 \).

05

Compare US and GB Perceptions

Comparing the probabilities: \( P_{US}(No) = 0.4533 \) and \( P_{GB}(No) = \frac{43}{100} = 0.43 \), there isn't a significant difference in the perception of inadequate protection. However, a much larger portion of GB investors is unsure, combined with those saying 'No' to make significant contrast with the US's perception.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

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

Survey Analysis

When conducting a survey analysis, it's important to understand the collected data. This involves not just gathering responses, but also analyzing the distribution of answers across different groups. For the survey in question, we have two distinct groups: investors from the United States and investors from Great Britain. Each group was asked whether they believed their government was protecting investors adequately. Their responses fell into three categories: Yes, No, or Unsure.
To effectively analyze the survey, we first categorize and count the responses.

• In the US, 48 investors answered 'Yes', 68 answered 'No', and 34 were 'Unsure'.
• In Great Britain, 21 answered 'Yes', 43 'No', and 36 'Unsure'.

Analyzing these responses helps in understanding the general sentiment among investors in each country towards government protection.

Investor Perception

Understanding investor perception is crucial in evaluating the effectiveness of government policies. The survey gives us a snapshot of how investors view the level of protection offered by their respective governments. For this analysis, the focus is on those who answered 'No' or 'Unsure', as they indicate a lack of confidence in government protection.
By analyzing the probability of responses, we get an idea of the general perception. In the US, about 45.33% of investors believe their government does not protect them adequately, while in Great Britain, this perception is slightly lower at 43%. However, when combining 'No' and 'Unsure' responses, a significant 79% of GB investors express doubt or lack of confidence compared to US investors. This indicates a stronger sense of uncertainty among British investors.

Government Protection

The concept of government protection in the context of investments involves regulations and safeguards that ensure investors are treated fairly and are protected from fraudulent activities. The survey in this discussion aims to measure how well these protections are perceived by the investors they aim to protect.
Government protection can take many forms, including regulatory oversight, investor education programs, and legal frameworks that protect investors' rights. However, investors' perception of these protections can significantly impact their confidence and willingness to invest. If investors feel inadequately protected, they might shy away from investment opportunities or demand higher returns to compensate for perceived risks. This highlights the importance of governments actively working to instill confidence amongst investors through transparent and effective protection measures.

Statistical Comparison

Statistical comparison involves looking at the probabilities and numbers derived from survey responses to draw meaningful conclusions. In this scenario, after calculating the probabilities of investors from the US and GB thinking their governments are not protecting them adequately, we compare these numbers.
Initially, it seemed there is no significant difference in perception between the US and UK investors as roughly 45.33% of US investors and 43% of GB investors feel inadequately protected. However, the inclusion of 'Unsure' responses from UK investors paints a richer picture. When these are included, we see a substantial 79% of British investors expressing uncertainty or dissatisfaction. This discrepancy showcases a deeper level of skepticism among British investors compared to their US counterparts, which is significant in understanding the overall sentiment regarding government protection. These statistical insights are important for policymakers as they highlight areas where more could be done to reassure and protect investors.