Investing in Arketia.

Dow, James ; Johnson, Gordon

CASE DESCRIPTION

The primary subject matter of this case is the integration of statistics, macroeconomics, and business ethics. Secondary issues include descriptive statistics (interpretation of standard deviation), normal distribution, and statistical hypothesis testing. The case has a difficulty level of three, appropriate for junior level. The case is designed to be taught in three class hours, including a formal case presentation by a team and a challenge by another student team. Three hours of outside preparation by students are required.

CASE SYNOPSIS

Students must balance bottom-line financial criteria against ethical issues of social responsibility as they decide if they should invest in one of two developing countries. East Arketia has a poorly educated work force, an inefficient government, and may not enforce property rights, but it has a democratic government with free speech protection. West Arketia is undemocratic, without free speech, but has a pro-business economic policy and a higher education level compared to East Arketia.

Students interpret the standard deviation in terms of the "gap between the rich and the poor" and use the normal area table to estimate the proportion of households below the poverty level in each country. In addition, they use hypothesis testing to estimate average household disposable income, as well as the proportion of prisoners who are political prisoners.

In the economics question, students evaluate the potential for growth in the two countries. The last question asks students to apply ethical principles to their decision, with specific references to the issue of the alternative political systems. "Does your company have an obligation to support the more democratic political regime of East Arketia, even if it turns out that returns to your firm will be lower?"

INSTRUCTORS' NOTES

RECOMMENDATION FOR TEACHING APPROACHES

We schedule a 40 minute coaching session to review needed concepts from our freshman business statistics class: interpretation of standard deviation, normal area table, hypothesis testing (mean and proportion). Less time is needed for freshman macroeconomics and ethics.

On the day students present the case, most of the class discussion is about ethical issues since the statistics is cut and dried.

1. Statistics provided by developing countries are not always reliable. Data can be hard to gather and is sometimes reported incorrectly. From your analysis of West Arketia, you conclude that citizens there average $1100 per month in household disposable income. The Minister of Development for East Arketia says that disposable income is the same in his country. To see if the data supports this, your company has randomly sampled 100 households from East Arketia and obtained data on household disposable income. The sample has a mean of $923.62 and a standard deviation of $ 84.64. Test the hypothesis, at the 1% significance level, that East Arketia also has a mean monthly household disposable income of $1100. (5 pts.)

This question uses the distribution of the sample mean, and students use sample data to make inferences.

[H.sub.0]: [mu] (population mean) = (or [greater than or equal to]) 1100 (the East Arketia claim) [H.sub.A] or [H.sub.1]: [mu] < 1100 (the West Arketia claim)

This is a "one tail" test since West Arketia wins the debate only if the mean for East Arketia is less than $1100. If the mean for East Arketia were more than $1100, East Arketia would win.

It is acceptable to use either the Z table (normal table) or the t table. Some texts insist that you must use the t table when you do not know the population standard deviation, but most texts allow the normal approximation when n is greater than 30. The Z table will be used here. With a one tail test, the Z table shows a critical Z = 2.33, with 1% significance. We will make the mistake of agreeing with West Arketia when East Arketia is truthful only 1% of the time.

The test statistic is: Sample Z = (Sample mean - population mean)/standard error of the mean.

The sample mean = $923.62, the hypothesis gave us population mean = $1100; and the standard error of the mean = (standard deviation/square root of sample size) = 84.64/10 = 8.464. The Sample Z = (923.62-1100)/8.464 = -20.8. Since the absolute value or +20.8 > 2.33, one rejects the null hypothesis. The population mean of East Arketia is significantly less than $1100, so it is reasonable to conclude that average East Arketia income is less than average West Arketia income.

2. Suppose East Arketia's government now reports that its population mean disposable household income is $925 per month, with a standard deviation of $70. West Arketia's population mean is $1100, with a standard deviation of $350.

a. Which country has more variation in income? Explain using popular phrases, such as "gap between rich and poor." (10 pts.)

Since the standard deviation of West Arketia = $350, while the standard deviation of East Arketia = $70, it can be concluded that West Arketia has more variation in income than East Arketia, hence a bigger gap between rich and poor.

b. Each country defines the poverty level to be $800. If you assume that income has a normal distribution, find the probability that a household's income is below the poverty level in

i. West Arketia

ii. East Arketia

Does it seem reasonable to assume a normal distribution? Is income symmetric or skewed? (10 pts.)

This question uses population data; unlike Q1, there are no sample statistics. Q1 and Q2 are intentionally in reverse sequence from the table of contents of most statistics text books. This simulates real-world applications.

(i) Probability that income is less than poverty level = P(income < 800) = P(Z < (800-1100)/350) = P(Z< -0.86) = .1949 from the normal table, so about 20% are below poverty level in West Arketia.

(ii) For East Arketia, P(Z < (800-925)/70) = P(Z < -1.79) = .0367, so about 4% are below the poverty level.

It is usually NOT the case that income is normally distributed because income is typically positively skewed to the right, that is the very wealthy create a right tail. In other words, mean > median because the mean is more likely to be affected by extreme values (the rich).

3. In explaining why their country is an attractive place to invest, the Minister of Commerce from West Arketia has argued that the political problems have been exaggerated and that fewer people have been imprisoned for political reasons than you have been led to believe. However, Amnesty International reports that one third of the prisoners in West Arketia are political prisoners. A representative from your company visited a prison and sampled 500 prisoners in West Arketia, concluding that 100 of them are political prisoners. Test the hypothesis, at the 10% significance level, that one third of the prisoners in West Arketia are political prisoners. Does this data support the Minister of Commerce or Amnesty International? What other issues might be important when evaluating this data? (20 pts.)

[H.sub.0]: p (population proportion) = (or [greater than or equal to]) 1/3 (the Amnesty International hypothesis)

[H.sub.A] or [H.sub.1]: p < 1/3 (the Minister of Commerce hypothesis)

If p is equal to or more than one third, that would support Amnesty International, so we have a one-tail test. At the .10 significance level, the critical Z = 1.28, using the normal approximation to the binomial. The test statistic is: Sample Z = (sample proportion--population proportion)/standard error of proportion. The sample proportion is 100/500 = .20, and the population proportion is 1/3 = 0.33, if the null hypothesis (Ho) is true. The standard error of the proportion is the square root of (.33)(1-.33)/500, which is the square root of .00044, namely .021. Hence Sample Z = (.20-.33)/.021 = -6.3. Since 6.3 is greater than 1.28, we reject the null hypothesis that one third of the prisoners are political prisoners. This supports the Minister of Commerce since 20% is significantly less than 33%.

The final part of this question is open-ended and is designed to get students to think about the context of the data. Unlike the income measure, which was objective, the classification of political vs. non-political is subjective. What is free speech to one person could be inciting a riot to the government. Another prisoner might be in jail for bank robbery, while critics of the government claim the prisoner is innocent and framed by prosecutors because of his political activity. Furthermore, the sample of prisoners might have been determined by the government, which has an incentive to provide a biased sample.

4. Based on the economic and statistical issues, evaluate the potential for growth in the two countries. (20 pts.)

Factors that determine Gross Domestic Product per capita include the level of physical capital, human capital, technology, and efficiency. Rapid economic growth requires investment in plant and equipment, an educated work force, recent technological innovations, and a government which does not delay development with bureaucratic hurdles, The output of a country is determined by the technology available, the amount of inputs used in production and how efficiently the inputs are used. Economic institutions, such as a legal system that enforces property rights and a government that is not too corrupt, are major factors in determining efficiency.

East Arketia has had relatively low investment in physical capital and human capital (the education of the work force) and has an inefficiently run government with a mixed record of enforcing property rights.

West Arketia has been better record in terms of policies that encourage economic efficiency and accumulation of inputs and so is likely to grow faster. In terms of return to the company, West Arketia would be a better choice.

5. Westman, Inc. also wanted to know whether economic growth could reduce income disparity and problems with poverty. You collected data from 20 countries and found that 6 had rapid economic growth, 8 currently have a major poverty problem, and 1 had both rapid economic growth and a major poverty problem.

a. Given rapid growth, what is the conditional probability of a major poverty problem?

Let A: growth, B: poverty, P(A)=6/20=.30, P(B) = 8/20= .40, P(A and B) = 1/20=.05.P(B/A) = P(A and B)/P(A) = .05/.30 = .17

b. Are the two events independent? Justify your answer.

P(B/A) not equal to P(B), so A and B are NOT independent.

c. If you are concerned about poverty, would prospects of economic growth affect your concern? How might this relate to the Arketia region?

Economic growth should reduce poverty, which is an argument for West Arketia. With economic growth, probability of poverty drops from .40 to .17. Students with more advanced training or interest in economics could discuss the possible connections between growth, poverty, and income distribution.

6. Some managers at Westman were concerned about arbitrary definitions of "rapid" growth and "major" poverty problem. A new sample was taken from 6 countries which report more precise data. The new data are:

X 4 6 5 2 1 8
Y 23 18 24 32 28 7

where X = percentage economic growth and Y = percentage households below the poverty line.

a. Find the regression equation to estimate Y given X

Y = 35.52--3.12X

b. If a country has a 3% growth rate, estimate the percentage below the poverty line.

Y = 35.52 -3.12(3) = 26, so 26% below the poverty line.

c. How does this affect your decision regarding the Arketia region?

As the growth rate increases, poverty decreases. Each additional one per cent increase in growth reduces the per cent below the poverty line by 3.12 percentage points. This supports the case for West Arketia.

7. If it is found that economic prospects are better in West Arketia, should Westman invest there? Or, does the company have an obligation to support the more democratic political regime of East Arketia, even if it turns out that the returns to the firm will be lower? To what extent are ethical issues relevant to your recommendation? (20 pts.)

Some ethical considerations include:

1. Who benefits and who loses from Westman's decision?

2. Who does Westman have a responsibility to? Only the shareholders? Other stakeholders?

3. What are those responsibilities?

Faculty teaching this case have reported that today's business majors have difficulty looking beyond the shareholders. Questions about historical business ethics issues, such as the boycott of South Africa, are met with bewilderment. This case is designed to reintroduce some of these issues.

The case was set up so that there was a stark contrast between the countries. West Arketia provides the better prospects for investment but has a worse record on human rights, while East Arketia is the reverse.

There is no right or wrong answer to this question independent of the ethical framework held by the student. A good answer would tie the decision to the student's belief about the responsibilities of companies.

James Dow, California State University, Northridge Gordon Johnson, California State University, Northridge