In the United States, according to a 2018 review of National Center for Health Statistics information, the average age of a mother when her first child is born in the U.S. is 26 years old. A curious student at CBC has a hypothesis that among mothers at community colleges, their average age when their first child was born is lower than the national average. To test her hypothesis, she plans to collect a random sample of CBC students who are mothers and use their average age at first childbirth to determine if the CBC average is less than the national average.

a.) State this study as a formal hypothesis test.

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b.) How would the student make a Type I Error in this study?

The curious student gathers her sample. She ends up with a random sample of 22 mothers at CBC. Among her sample, she finds their average age at first childbirth is 24.4 years old, with a standard deviation of 3.6 years. Help our curious student make a decision at the ?? = 0.05 level.

c.) Calculate the Test-Statistic for the test.

d.) Calculate the Critical Value for the test.

e.) Approximate the p-value.

f.) What is your decision? Be sure to interpret your decision in a way that would make sense to someone that is not a statistician.

63% of owned dogs in the United States are spayed or neutered. Round your answers to four decimal places. If 32 owned dogs are randomly selected, find the probability that

a. Exactly 21 of them are spayed or neutered. Incorrect
b. At most 19 of them are spayed or neutered. Correct
c. At least 20 of them are spayed or neutered. Correct
d. Between 15 and 20 (including 15 and 20) of them are spayed or neutered. Incorrect

Suppose the current exchange rate is $1.42/€, the interest rate in the United States is 4.00%, the interest rate in the EU is 6%, and the volatility of the $/€ exchange rate is 20%.

(a). Using the Black-Scholes formula, calculate the price of a three-month European call option on the Euro with a strike price of $1.45/€.

The price of a three-month European call option is-------- $ (round to five decimal places).

The mean cost of domestic airfares in the United States rose to an all-time high of $400 per ticket. Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $100. Use Table 1 in Appendix B.

a. What is the probability that a domestic airfare is $540 or more (to 4 decimals)?

b. What is the probability that a domestic airfare is $260 or less (to 4 decimals)?

c. What if the probability that a domestic airfare is between $300 and $470 (to 4 decimals)?

d. What is the cost for the 3% highest domestic airfares? (rounded to nearest dollar)
$

The mean cost of domestic airfares in the United States rose to an all-time high of $400 per ticket. Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $100. Use Table 1 in Appendix B.

a. What is the probability that a domestic airfare is $540 or more (to 4 decimals)?

b. What is the probability that a domestic airfare is $260 or less (to 4 decimals)?

c. What if the probability that a domestic airfare is between $300 and $470 (to 4 decimals)?

d. What is the cost for the 3% highest domestic airfares? (rounded to nearest dollar)
$

In November (and, technically, December) of 2016, Donald Trump was elected President of the United States, regardless of the fact that Hillary Clinton won nearly 3 million more votes. This reminded many Americans that the president is elected by the Electoral College, not by the public; thus, rather than DIRECTLY electing the president, we (At best) indirectly elect them. What I ask you is this: in terms of the principal-agent relationship this establishes, does this give the public sufficient control over the presidency? Why, or why not?

Downtown Street, a British Company, is considering establishing an operation in the United States to assemble and distributes top hats. The initial investment is estimated to be £20,000,000 (British pounds - GBP) which is equivalent to US$23,000,000 at the current exchange rate. Given the current corporate income tax rate in the United States, Downtown Street estimates that total after-tax annual cash flow in each of the three years of the investments life would be US$10,000,000, US$12,000,000, and US$15,000,000, respectively. However, the U.S. national legislature is considering a reduction in the corporate income tax rate that would go into effect in the second year of the investment’s life, and would result in the following total annual cash flows: US$10,000,000 in year 1, US$14,000,000 in year two, and US$18,000,000 in year three. Downtown Street estimates the probability of the tax rate reduction occurring at 50%. Downtown Street uses a discount rate of 12% evaluating potential capital investments. Present value factors are as follows:

Period PV Factor

1 0.893

2 0.797

3 0.712

The U.S. operation will distribute 100% of its after-tax annual cash flow to Downtown Street as a dividend at the end of each year. The terminal value of the investment at the end of three years is estimated to be US$25,000,000. Neither the dividends nor the terminal value received from the U.S. investment will be subject to a British income tax.

Exchange rate between GBP and USD are forecasted as follows:

Year 1 GBP 0.74 = USD 1.00

Year 2 GBP 0.70 = USD 1.00

Year 3 GBP 0.60 = USD 1.00

Determine the expected net present value of the potential US investment from a parent company perspective.

Fresh!Now! is a chain of grocery stores in the United States with 1394 grocery stores in total, some of which also sell bakery goods and freshly made food-to-go. Fresh!Now!’s goal is to provide good quality fresh vegetables at affordable prices. However, given the existing market of organic food supplies, Fresh!Now! is facing tremendous competition. They realize that Fresh!Now! has to make their stores more attractive to customers.

In 19 stores across Massachusetts and New York, they have implemented a new concept to present the vegetables in the stores and have collected information of the average daily profit of leafy vegetables (in dollar) per customer per store (see table below). Janine, the head of the analytics department at Fresh!Now!, has tasked you with developing an anlaysis to better understand if the new concept has any effect.

Your first task it to create a 95% confidence interval for the mean of the dataset using the sample collected from Massachusetts and New York.

What is the upper limit of this confidence interval?

Round your answer to three decimals places (e.g. if your calculation results in 12.9237 put in 12.924).

What is the lower limit of this confidence interval?

Round your answer to three decimals places (e.g. if your calculation results in 12.9237 put in 12.924).

Part2

To understand if the new concept has taken effect, you want to conduct a hypothesis test. Average daily profit per customer per store for the leafy vegetables in all other Fresh!Now! grocery stores is 13.5.

You formulate the following hypothesis test:

H0: Average daily profit at Fresh!Now! in the New York/Massachusetts stores is not higher than the average daily profit of all other Fresh!Now! grocery stores at a confidence level of 95%.

H1: Average daily profit at Fresh!Now! in the New York/Massachusetts stores is higher than the average daily profit of all other Fresh!Now! grocery stores at a confidence level of 95%.

Calculate the test-statistic for the hypothesis test above.

Round your answer to three decimal places (e.g. if your calculation results in 12.9237 put in 12.924).

1. (15 pts) 52% of adults in the United States are women and 48% are men. The heights of the men follow an approximately normal distribution with mean 69.1 inches and standard deviation of 2.9 inches. The heights of the women are approximately normally distributed with mean 64.5 inches and a standard deviation of 2.7 inches. Suppose that we select 10 adults at random from the U.S. population.

If a simulation produced a random selection of 10 adults with

The average height as 68.186572 inches

Max height of 73.16397 inches

A) Calculate the 95% prediction interval for the average height of a random sample of 10 adults

B) Calculate 95% prediction interval for the maximum height of a random sample of 10 adults.

(20.4) The exchange rate between the United States of Albion (U.S.A.) and the Republic of Oz is now 1:1 with inflation in both countries expected to be 2% and interest rates 4%.

What does PPP imply about the exchange rate in 20 years time?

If inflation in the U.S.A. increases to 3% how does your answer change?

What happens to the current exchange rate if U.S.A. interest rates rise to 5% along with inflation increasing to 3%?