1. In the United States, the estimated annual probability that a woman over the age of 35 dies of lung cancer is 0.001304 for current smokers and 0.000121 for non-smokers.   

(a) Calculate and interpret the difference in the proportions and the relative risk. Which is more informative for these data? Why? (b) Calculate and interpret the odds ratio. Explain why the relative risk and the odds ratio take on similar values.

2. For people with a particular type of cancer, the odds ratio for recovery (cancer in remission) between age groups (young versus old) was 4.5.   
(a) Choose one correct interpretation:

i. The probability of recovery for young subjects is 4.5 times the probability of recovery for old subjects. ii. The probability of recovery for old subjects is 4.5 times the probability of recovery for young subjects. iii. The odds of recovery for old subjects is 1/4.5 = 0.22 times the odds of recovery for young subjects. iv. The odds of recovery for old subjects is 4.5 times the odds of recovery for young subjects.


(b) Suppose that the odds of remission for young subjects is 3.1. For each age group, find the proportion of subjects who went into remission.

(c) Find the value of R in the interpretation: “The probability of remission for young subjects is R times that of older subjects.”

1. On a recent trip to the united States, you purchased a ticket in a state lottery. Now you discover that you are the lucky winner of the $30 million prize. You can take your prize money either as (a) 30 payments of $1 million per year (starting today), or (b) $15 million paid today. If the interest rate is 8%, which option should you take. Show calculations

2. James has just turned 35 years old, and he has decided it is time to plan seriously for his retirement. On each birthday, beginning in one year and ending when he turns 65, he will save $10,000 in an RRSP account. If the account earns 10% per year, how much will James have saved at age 65.

Plan B is the common name in the United States and Canada for the emergency contraception drug levonorgestrel. The high dose of progestogen it delivers has been shown in the lab to inhibit ovulation, thus rendering fertilization impossible. Some groups, however, are concerned that if the drug interfered with the fertilized egg, it could be considered abortive rather than strictly contraceptive. Researchers enrolled a cohort of fertile women attending a family planning clinic for emergency contraception after unprotected intercourse during their fertile period. From interviews, blood samples, and ultrasounds, the researchers were able to establish the time of intercourse relative to the women's menstrual cycles. In this cohort, 8787 women had unprotected intercourse before ovulation (pre‑ovulation group) and 3535 women had unprotected intercourse on or after ovulation (post‑ovulation group). Based on standard clinical assessments of fertility rates by day of the menstrual cycle, the researchers expected 13.313.3 pregnancies in the pre‑ovulation group and 7.07.0 pregnancies in the post‑ovulation group. Instead, they observed 00 and 66 pregnancies, respectively.

(a) We want to know if there is evidence that Plan B impacts the chance of pregnancy when taken before ovulation. What are the observed and expected counts of pregnancy and no pregnancy in the pre‑ovulation group? (Enter your answers rounded to one decimal place.)

Pregnancyobserved=Pregnancyobserved=

Pregnancyexpected=Pregnancyexpected=

No pregnancyobserved=No pregnancyobserved=

No pregnancyexpected=No pregnancyexpected=

Use these counts to compute the chi‑square statistic. (Enter your answer rounded to two decimal places.)

?2=χ2=

Select the correct response to whether or not the test assumptions met.

The expected counts are not large enough, so the test assumptions are not met.

A cohort can be considered a random sample and the expected counts are large enough, so the test assumptions are met.

A cohort cannot be considered a random sample, so the test assumptions are not met.

Neither the cohort can be considered a random sample nor the expected counts are large enough, so the test assumptions are not met.

Calculate the degrees of freedom. (Enter your answer as a whole number.)

df=df=

Find the ?P‑value. (Enter your answer rounded to six decimal places.)

?P‑value ==

Select the correct conclusion.

None of the options are correct.

There is very strong evidence that Plan B impacts the chance of pregnancy when taken before ovulation.

The study found weak evidence that Plan B impacts the chance of pregnancy when taken before ovulation.

The study failed to find evidence that Plan B impacts the chance of pregnancy when taken before ovulation.

(b) We want to know if there is evidence that plan B impacts the chance of pregnancy when taken after ovulation. What are the observed and expected counts of pregnancy and no pregnancy in the post‑ovulation group? (Enter your answer rounded to one decimal place.)

Pregnancyobserved=Pregnancyobserved=

Pregnancyexpected=Pregnancyexpected=

No pregnancyobserved=No pregnancyobserved=

No pregnancyexpected=No pregnancyexpected=

Use these counts to compute the chi‑square statistic. (Enter your answer rounded to two decimal places.)

?2=χ2=

Select the correct response to whether or not the test assumptions met.

A cohort can be considered a random sample and the expected counts are large enough, so the test assumptions are met.

Neither the cohort can be considered a random sample nor the expected counts are large enough, so the test assumptions are not met.

The expected counts are not large enough, so the test assumptions are not met.

A cohort cannot be considered a random sample, so the test assumptions are not met.

Calculate the degrees of freedom. (Enter your answer as a whole number.)

df=df=

Find the ?P‑value. (Enter your answer rounded to four decimal places.)

?P‑value ==

Select the correct conclusion.

The study failed to find evidence that Plan B impacts the chance of pregnancy when taken after ovulation.

None of the options are correct.

The study found weak evidence that Plan B impacts the chance of pregnancy when taken after ovulation.

There is strong evidence that Plan B impacts the chance of pregnancy when taken after ovulation.

(c) Select the correct description of the study findings and what they suggest about the mechanism of action of the Plan B drug.

There is no evidence that Plan B prevents pregnancy when taken before ovulation or after ovulation. These findings reject the theory that Plan B works by inhibiting ovulation.

There is very strong evidence that Plan B prevents pregnancy when taken after ovulation but not when taken before ovulation. These findings support the theory that Plan B works by inhibiting ovulation.

There is weak evidence that Plan B prevents pregnancy when taken before ovulation but not when taken after ovulation. These findings support the theory that Plan B works by inhibiting ovulation.

There is very strong evidence that Plan B prevents pregnancy when taken before ovulation but not when taken after ovulation. These findings support the theory that Plan B works by inhibiting ovulation.

The current guidelines for companies in the United States is GAAP while many areas of the world have adopted IFRS. The SEC is in favor of a single accounting standard. Your company is trying to decide which guidelines to follow. What factors should your company consider in determining which set of standards it should follow? What advantages and disadvantages do you see with following each method?

Suppose interest rates in the United States, but they don’t rise in other nations. As a result of this change

The U.S. dollar appreciates

The U.S. dollar depreciates

U.S. exports will increase

U.S. imports will decrease

Price levels in the unites states will increase

Suppose Americans began purchasing real assets in Europe. How would this impact the foreign exchange market for the euro and the dollar price of the euro?

Decrease/increase

Increase/ decrease

Increase/increase

Decrease/Decrease

Decrease/Not change

Suppose interest rates rise in the United States, but they don’t rise in other nations, what is the impact of flow of the financial capital, the value of the dollar, and U.S. net export (based on the changing value of the dollar)?

Capital flow/ Value of the U.S. dollar/ Net exports

Inflow/appreciate/Increase

Inflow/appreciate/decrease

Inflow/depreciates/increase

Outflow/depreciates/increase

Outflow/appreciates/decrease

If the U.S experiences an increase in exports, ceteris paribus, then

The U.S. dollar will appreciate because of increased supply of U.S. dollars by foreign nations

The U.S. dollar will depreciate because of increased supply of U.S. dollars by foreign nations

The U.S. dollar will appreciate because of increased demand of U.S. dollars by foreign nations

The U.S. dollar will depreciate because of increased demand of U.S. dollars by foreign nations

The U.S, dollar will depreciate and the U.S will import more foreign goods

The table below shows the life expectancy for an individual born in the United States in certain years.

1. Find the estimated life expectancy for an individual born in 1973

2. Use the two points in part (e) to plot the least squares line on your graph from part (b).

3. Are there any outliers in the data?Yes, 1930 and 2010 are outliers.Yes, 1930 and 1950 are outliers.     Yes, 1950 is an outlier.No, there are no outliers

4. Using the least squares line, find the estimated life expectancy for an individual born in 1870. (Round your answer to one decimal place.)
Does the least squares line give an accurate estimate for that year? Explain why or why not. Yes, because the estimate is over 50 years.No, because 1870 is outside the domain of the least squares line.    

On a separate sheet of paper, draw a Lorenz Curve for the United States, using the 2017 values for income quintiles. Label each kink point carefully, and draw the diagonal equality Lorenz Curve. Calculate the Gini Coefficient, and show your work. This is a long and tedious math problem, where you find the areas of triangles, rectangles and trapezoids over and over to get the areas needed for the formula.

2017: Shares of aggregate income

A firm manufactures a product in the United States. Its costs of production and shipping are $100. It sells the product in Silliestan for 1000 Zlotys which is equivalent to $500 (2 Zlotys = $1). Costs of distribution and selling in Silliestan are $100 (200 Zlotys) so the firm has a profit of $300. Within the next year, the Zloty is expected to fall from 2 Zlotys to the dollar to 4 Zlotys to the dollar while inflation in Silliestan is expected to be 100%. US costs, in dollars, are not expected to change.

Show all calculations. No points for the correct answers without calculations.

a) Given these expected changes, how many Zlotys will it cost, in total, to make the product in the United States and to sell it in the foreign country? The total costs of manufacture, shipping and sales will be ______________________ Zlotys. 2 points

b) If you sell the product for 1000 Zlotys, how much would your profit or loss be? ________ Zlotys 2 points

c) What other factors should be taken into account when setting a price? Be specific. 1 point.

d) If your company sells the same product in a neighboring country for a higher price, this would give rise to a ____________________ market. 1 point

e) If the foreign country were to ask your firm to take partial payment in a local product, say turnips, this would be an example of ________________________ . 1 point.

The heights of women aged 20 to 29 in the United States are approximately Normal with mean 65.1 inches and standard deviation 2.7 inches. Men the same age have mean height 70.2 inches with standard deviation 2.9 inches. NOTE: The numerical values in this problem have been modified for testing purposes. What are the z-scores (±0.01) for a woman 6 feet tall and a man 6 feet tall? A woman 6 feet tall has standardized score A man 6 feet tall has standardized score

QUESTION 2:

Use Table A to find the proportion of observations from a standard Normal distribution that satisfies each of the following statements. Give your answers to four decimal places.

a)  z < -0.77=

b) z > -0.77=

c)  z < 1.31=

d) -0.77 < z < 1.31=