Business Data Analysis Computer Applications Project - AFE135 - Statistics Assignment Help

Assignment Task

Q1 – Share Prices for Tech Companies
The file shares.xls contains weekly share prices for two tech companies – AMZN (Amazon) and APPL (Apple) over the last five years. The weekly percent returns in these series are also provided in the adjacent columns. Your task is to analyse these data from the perspective of a potential investor who is interested in both maximising returns but also minimising risk.
Produce some line charts showing the performance of these two firms over 2016-2021. Which company do you think had the better year?
Produce some histograms showing the distribution of the weekly returns in price. Interpret the results. If a client wishes to invest and is extremely concerned with minimising potential losses, which company would you recommend? Conversely, if a client is mostly interested in growth potential, which investment would you recommend?
Calculate the mean, standard deviation and skewness of the two weekly returns variables. Discuss these variables in the context of financial risk and return.
Summarize the risk/return trade-offs for the weekly change series using the Coefficient of Variation. Interpret these statistics. Which investment is preferred?
Write a couple of sentences contrasting a hypothetical positive (right) skew investment from a hypothetical negative (left) skew investment (again using weekly changes). Which investment is more likely to report large losses? Which is more likely to post frequent small gains?
Consider the two theories below about the relationship between AMZN and APPL prices. Theory 1 says that both are tech companies and are mostly affected by common factors (e.g. demand for tech products), which suggests the prices should be positively associated. Theory 2 claims that AMZN and APPL are competitors, and therefore one firm’s loss is the other’s gain. This suggests the variables should be negatively related. Using a scatterplot for the weekly change variables, summarize the statistical evidence on this issue. Which theory do the data support? Briefly discuss.

Q2 – Accidents and Full/New Moons
It is sometimes claimed that full or new moons have strange effects upon human psychology, resulting in increased risk-taking and other forms of unusual behaviour. If this is the case, we may expect to see the effects show up empirically in data sets related to human activity. The file moon.xls has data on daily hospital admissions for accidents, stratified by whether or not there was a lunar/astronomical event taking place on the day of admission. The idea here is that if full/new moons (and other related spooky phenomena) cause people to act erratically, then there are likely to be more accidents, and therefore more hospitalisations, on those days. The first column gives admission counts for weekdays where there was no lunar/astronomical event taking place, and the middle column shows totals on weekdays where there was such an event. The column on the right gives admission counts over weekends. Note that since weekends have fewer days, the column here is shorter, and contains both full moons and non-full moon data.
Your first task is to determine whether or not there are any meaningful differences between the data observed on astronomically important days and non-astronomically important days. Secondly you are to see if there are differences between accident rates on weekdays and weekends.
Compare the first two variables (weekday admissions and full/new moon admissions) using histograms, means, standard deviations and coefficients of skewness. Report the results, and discuss any differences/similarities that you observe. Are there more hospital admissions on astronomically important days?
Do we expect to see large differences in the distributions of these variables? Why or why not?
Do you think that sampling variation could explain any small differences that you observe? Write a short paragraph explaining why or why not.
Perform the same analysis (histograms, means, standard deviations, skewness) using data comparing admissions on weekends and weekdays.
Do the results line up with your expectations? Are the distributional differences between weekdays and weekends likely to be statistically meaningful?

Q3 – Serology Tests for Covid
Mapping the rates of infection of Covid-19 is a critical task for public health professionals. Geographical locations that have had high fractions of their populations infected may be close to herd immunity, while places that have had very few infections may see surges in the future. Your task in this question is to perform some analysis using a simulated serological dataset on diagnosing exposure to Covid. The data are available in the file covid.xls.
Suppose you take a random sample of 381 individuals from a town in the USA, and you find that 88 individuals report positive antibody results. Calculate the sample proportion for positive antibodies, the standard error of this proportion, and provide a 90% interval for the true population proportion. You can use the calculator tab named CI Categorical to answer this question.
Calculations such as those performed above require normality assumptions that are only approximations. Is your assumption of normality appropriate in this instance? Why or why not?
Briefly discuss what happens to this interval if (i) the sample size were to increase, and (ii) if the confidence level was changed from 90% to 95%. Provide some intuition for your answers.
To model herd immunity, epidemiologists use the formula H=1-1/R0. Here H lies between zero and one and is the fraction of the population that needs to be immune, and R0 is the base reproductive rate (the average number of transmissions per infection at the start of an epidemic. Suppose an epidemiologist produces a confidence interval for R0 of 4.0±0.5. Calculate the corresponding interval for H. Is your town near the herd immunity threshold?
In order for your analysis to be generalizable to a larger population, it is important to ensure your sample resembles that population. Suppose that the average age of the town that you are analysing is known to be 43, the average income is $66,000 per year, and the average years of formal education is 14.2. How closely does your sample match these population parameters? Would you have any reservations about your sample not being appropriately representative? Discuss.
Formally test the hypothesis (using a t-test) that the average age is 43 using your data. Present the null and alternative hypotheses, the test statistic, a critical value and a conclusion. You can use the calculator tab named hypothesis test continuous to answer this question. Briefly discuss whether or not this test indicates your data may be unrepresentative.

Q4. Infant Mortality
One of the most important tasks for development organizations such as the World Bank is to construct policy that lowers infant mortality in poorer countries. The file infant_mort.xls has data on global infant mortality rates in deaths per thousand live births. Also included are some variables potentially related to infant mortality including GDP per capita, the number of physicians per 1000, and the average number of years of education. Also included are (i) measures of sanitation quality, and (ii) measures of contraceptive access.
Produce scatter plots linking infant mortality to each of these potential explanatory factors. Which ones appear to be most strongly correlated with mortality rates?
The plot of GDP per capita and infant mortality has an unusual feature that complicates our linear modelling techniques. Discuss this feature and its implications for correlation/regression analysis.
Regress infant mortality separately against all five covariates (i.e. produce five regressions) and report your results. Which variable is most significantly linked to mortality? (Hint, look at the p-values in your outputs).
Test the hypothesis that education is significantly correlated with infant mortality. State the hypotheses, test statistic, p-value, critical value, and a conclusion.
If you are an adviser to the World Health Organization, what types of policies would you recommend, based upon your analysis? Discuss.

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