商业分析quiz代考 Suppose some doctors have made the vaccine available to individuals who self-selected into receiving the vaccine. Can you think of
Instructions to candidates 商业分析quiz代考
This paper contains four questions. You may answer three OR four questions, but only your best THREE answers will count towards the final mark and each of those three answers will be given equal weight.
There are 99 marks available for this exam. The mark you achieve in the exam will be converted into a percentage and weighted accordingly when calculating the overall grades for the course.
Please answer each question in a separate answer booklet.
- Evaluating the impact of an online education technology Suppose you are a parent considering purchasing a new instructional technology for your child to use in a socially-distanced spring term. An educational technology company offers an online education technology (a combination of recorded videos and home exercises with live online instruction) to use in the spring. You email the company requesting any information they have on the performance of students who have used the technology in the past, and they provide you with data showing that students in schools that adopted their technology in the autumn have higher scores on a standardised examination than the national average.
a. Your first concern regarding the company’s evidence is that the test scores among students whose schools adopted the new technology may not be statistically significantly greater than the test scores among students whose schools did not adopt the new technology. Please explain this concern and suggest some evidence the company can provide to address the concern and make the case for statistical significance. [5 points]
b. Your next concern regarding the company’s evidence is that the test scores among students whose schools adopted the new technology may not be economically significantly greater than the test scores among students whose schools did not adopt the new technology. Please explain this concern and suggest some evidence the company can provide to address the concern and make the case for statistical significance. [5 points]
c. You next worry that the evidence of higher test scores presented by the company may not be causal due to omitted variable bias. Suppose you email the company requesting any information they have on the types of schools where the technology was adopted. They write back telling you that most schools that adopted the technology in the autumn term were poorlyfunded schools that could not produce their own online instruction. Does that response make you more convinced of the technology’s effectiveness? Explain, making reference to a path diagram. [5 points]
In addition to informing you about the characteristics of the schools that adopted the technology in the autumn, the firm tells you that they also have evidence from an experiment they conducted with a single large school district in the United States, in which children from some schools were randomly assigned the technology while children in other schools were randomly assigned to a control group without the technology.
The company emails you Stata output from an analysis of the experimental data, providing you with estimates of a simple regression with test scores as the outcome variable and as the explanatory variable, a dummy variable where 1 indicates that a school was in the treatment group and 0 indicates that a school was in the control group.
d. Are you concerned about the experiment being conducted in only one school district? If so, is this primarily an internal validity concern or external validity concern? Provide a short example illustrating your concern. [5 points]
e. Suppose the company states that the technology significantly improves test scores at the 5% level, calculated from a one-sided test. What should be the sign of the coefficient (that is, the slope) on the dummy variable? In the Stata output, what should you expect for the p-value of the coefficient (that is, the slope) on the dummy variable be? Explain. [8 points]
f. Are you concerned that the company did not provide you with results from a multiple regression (including school characteristics as control variables along with the experimental treatment dummy variable)? Explain, making reference to a path diagram. [5 points]
2. Testing a COVID vaccine
Suppose you run a biotech lab and you are planning to conduct an experimental test of a new COVID vaccine. You will conclude that the vaccine is effective if the proportion of infected subjects in the treatment group is far enough below the proportion of infected subjects in the control group.
a. What is a Type 1 error in this context? What is a Type 2 error? Why is each of these costly? [6 points]
b. Is there anything the lab can do to achieve both lower Type 1 and Type 2 error rates? Explain. [6 points]
c. Suppose some doctors have made the vaccine available to individuals who self-selected into receiving the vaccine. Can you think of an omitted variable that would make the vaccine’s impact look too small in an observational (non-experimental) analysis linking the vaccine to infection? Explain, using a path diagram. [5 points]
d. Suppose the vaccine may be evaluated in multiple trials. How would that affect the level of statistical significance you demand from each individual trial? Explain. [5 points]
e. Suppose you consider running the experiment inside a care home, with the vaccine being provided to a random subset of residents, while the others in the home are assigned to the control group – the individuals in the control group may benefit indirectly from the vaccine if the treated subjects are less likely to get (and spread) the virus. Is this design likely to have strong internal validity? Explain. [6 points]
f. Would running the experiment across care homes – with some care homes randomly assigned the vaccine and others randomly assigned to a control group provide a better estimate of the vaccine’s effects compared to the design in part (e)? Explain. [5 points]
3. Adopting a new AI technology 商业分析quiz代考
Suppose you are the CEO of a fintech (financial technology) company, considering investing in a new AI technology to improve the evaluation of loan applicants. The new technology is very expensive, but it should reduce the default rates on your company’s loans by making better predictions about the creditworthiness of loan applicants. Currently, 10% of loan applicants default. Your team of analysts tells you that adopting the new AI technology would be profitable for your company if the default rate (the proportion of borrowers who default) fell below 5% after
adopting the new technology.
In order to judge whether the new technology is likely to achieve this level of performance, you contract with the AI firm to conduct a “pilot” study on 1000 borrowers selected by the AI algorithm. Then, based on the results of the pilot, you will decide whether or not to adopt the new technology.
a. Specify the null and alternative hypotheses you will test using your pilot sample data. [2 points]
b. In this business problem, what is a Type 1 error? What is a Type 2 error? Use non-technical language. [2 points]
c. In terms of the pilot sample’s default rate, what decision rule (“action threshold”) should you use? Use a 10% significance level. Remember that sample proportions are distributed normally with a standard error of:
d. What is the power of this test if the true default rate (that is, population proportion) were 3.5% when the AI technology is adopted? [7 points]
e. Draw a sketch of the normal distribution curve that illustrates the power of the test when the true population proportion default is 3.5%. Your figure should correspond as closely as possible to parts (c) and (d) above, indicating the numerical values of the population proportion assumed to be true and the numerical value of the decision rule (action threshold) used, and you should clearly label the area corresponding to the power of the test. [4 points]
Your CFO does not like your decision rule or your statistical test, finding it too risky. She tells you that she wants the company to use a 5% significance level, and she also wants there to be only a 1% probability of a Type II error when the true default rate (population proportion) is 3.5%.
f. Which risks are mitigated by the CFO’s proposed test: type 1 error, type 2 error, both, or none of the above? Explain how this can be done. [4 points]
g. What is the minimum sample size you would need for a statistical test that would meet the CFO’s desired specifications? Show your work. [8 points]
4. Natural resources and the wealth of nations
Some eminent social scientists (James A. Robinson and co-authors in, “Political foundations of the resource curse,” Journal of Development Economics, 2006) have argued that greater natural resources can improve countries’ economic outcomes or worsen them, depending on the initial political institutions in place. They argue that when governments are accountable to their citizens, natural resource booms will improve economic outcomes, but when governments are unaccountable, one might see a natural resource “curse”, with outcomes worse in places with better endowments of natural resources.
Suppose you wish to test this hypothesis using cross-country data. Specifically, you estimate a multiple regression model using data from 100 countries. The outcome variable is GDP per capita in 2010 (called “GDP” in the dataset and measured in US dollars per capita), and the explanatory variables are:
Autocracy: a dummy variable equal to 1 if the country is classified as an autocracy (i.e., the government is unaccountable to its citizens) in the Polity dataset. The variable is equal to 0 if the country is classified as a democracy(i.e., the government is accountable to its citizens).
Resources: the dollar value of a country’s natural resource endowment, estimated by the US Geological Survey (the variable is measured in trillions of US dollars, so a one unit increase in the
variable indicates a $1 trillion greater stock of natural resources).
AutXres: interaction between the Autocracy dummy variable and the Resources variable.
The regression results are as follows (please note that these are based on fictional data!):
a. What is the predicted GDP per capita for a country that is autocratic (i.e., Autocracy = 1) and has a natural resource endowment worth $2 trillion? What about a resource-poorer autocracy with only $1 trillion in resources? [4 points]
As you should recall from lecture, the multiple regression model including the group (Autocracy) indicator, another explanatory variable (Resources) and the interaction,reproduces the simple regressions of GDP per capita on Resources for each value of the group variable.
b. Please write down the simple regression model (with the estimated slope coefficient and estimated y-intercept) predicting GDP per capita using Resources for democracies (Autocracy = 0).
c. Please write down the simple regression model predicting GDP per capita using Resources for autocracies (Autocracy = 1). [3 points]
d. Does the regression evidence support the argument made in the Journal of Development Economics article? Explain. [3 points]
e. True or False (and explain): The slope on the interaction variable does not tell you the effect of an additional trillion dollars of Resources in either democracies or autocracies.
True False [4 points]
f. What does the “_cons”coefficient estimate tell you? [2 points]
g. Show that this model always predicts that democracies (Autocracy = 0) will be richer than autocracies (Autocracy = 1) by graphing predicted income against resources for both democracies and autocracies. This prediction is clearly incorrect: some autocracies in fact are richer than some democracies. Does this make the model completely useless? Explain why or why not. [5 points]
h. True or False (and explain): The model suggests that autocratic institutions are more economically damaging in resource-rich countries.
True False [4 points]
i. Suppose you did not consider the role of political institutions in your model, predicting GDP per capita using Resources,for all countries, using a simple regression. Which of the following is the most likely coefficient on Resources?
Would this regression be informative regarding the impact of natural resources on economic outcomes? Please explain your answer. [5 points]