2013 UN YPP Statistics Short answers

Question 1: Suppose sum of Y = 2907, and sum of Y^2 = 150,000 (?).
a. Find the mean of Y.
b. Find the standard deviation of Y and derive a 95% confidence interval. I think you had to use the formula var(Y) = E(Y^2) -  E(Y)^2 in order to solve it, something like that! And, note that there were no t-tables, z-tables, or any sort of table attached to the test, so you had to remember that for a confidence interval, the z-value at 95% confidence would be 1.96.

Question 2: You are given a table of the market exchange rate between country A and B, and the price of a hamburger in both countries, for five different time periods.
a. Recalculate country A's hamburger prices in terms of country B's currency.
b. Find the purchasing power parity market exchange rate, something like that ??
c. Determine to what extent country B's currency is over or undervalued.

Question 3: can't remember!

Question 4: You are doing a survey for the country of Orangeland. Orangeland had 6 neighborhoods. All of them had roughly the same population, except for the neighborhood of Dylan, which had very few people.
a. if you do a simple random sample, what problem will you run into (I think they meant, you probably won't get any people in your sample who live in Dylan)
b. suppose you randomly selected 100 people from each neighborhood. What kind of sample is that?
c. suppose you randomly selected people from each neighborhood, but you did it proportionally to the population in the neighborhood. Will that sample be more or less precise than the sample in part b.
d. why might you want to choose the design in part b anyways?
Note: there were 2 more parts to this question, but I can't remember any more.
Note: thank God they did not want us to memorize the variance formulas for a stratified sample!

Question 5: this was about time series, residuals and Arima models
a. name the components of a time series.
b. write out the formula for an Arima(1 0 1) model. Include the residual, autoregressive, and moving average terms.
c. why should you seasonally adjust your time series?
d. how would you seasonally adjust your time series?

Question 6: multi-variable regression
You have a model Y = 700 + 17x_1 + 2x_2, where x_1 = advertising expenditures, x_2 = income levels, and y = sales. You also have the print-out from the statistical program that came up with that equation (Note: the coefficients in the equation are not identical to those on the test, just how I remember them.)
a. the statistical print-out had missing values. Fill them all out. This included filling out some of the degrees of freedom, some mean square error, all the t-values for the estimated coefficients, and maybe some other stuff.
b. do a significance test, at 95% confidence, for the estimated coefficients
c. do a significance test, at 95% confidence, for how well the two explanatory variables explain Y
d. you are given the R-squared value. Interpret what it means.

Question 7: You have a population growing at a rate of 0.2 and you are given N(2008).
a. use the formula N(t) = N(0)exp(rt) to find what the population will be in 2 years (I think this was the right formula; it was not given on the test, so we had to know it)
b. if the population tripled between 1978 and 2008, what would the growth rate have to be?

Question 8: probability
the probability that it snows tomorrow is 0.6, probability it rains is 0.4. P(late given it snows) = 0.4 and P(late given it rains) = 0.6 (I'm making these numbers up, I can't remember them!) What is the probability that I will be late tomorrow?

And this is what it was like to be at the UN taking the test!