The claim is that the IQ scores of statistics professors are normally​ distributed, with a mean less than 133. A sample of 11 professors had a mean IQ score of 130 with a standard deviation of 8. Find the value of the test statistic.

Aaron McCarthy

Aaron McCarthy is 28 years old and is making his first attempt at determining how much he needs to save each year in order to fund his retirement. He works for a Fortune 500 corporation as a project manager. His employer offers a 401(k) plan featuring a 1:1 match for every dollar contributed to a maximum of 6% of his salary. Aaron is eligible to participate but currently is not enrolled in the plan. He is in the 25% marginal tax bracket.

Based on an analysis of his last 3 annual cash flow statements, he has determined that his average gross income has been about $58,000 and his annual living expenditures have been about $46,700. He expects both his income and expenses to match an assumed inflation rate of 3.5% going forward indefinitely.

In order to be conservative, Aaron is working under the assumption that he will be able to maintain his current standard of living on 85% of his current spending after he retires (that is, he expects his annual expenses to fall by 15% in retirement without reducing or lowering his current standard of living).

According to the annual benefit statement he received before his last birthday, Aaron can expect to receive $15,000 (expressed in today’s dollars) per year in Social Security retirement benefits at his normal retirement age (67). Aaron plans to retire at age 67, and expects to live until age 90. His mother’s parents lived until their early 80’s, as did both his father’s parents.

Again, to be conservative, Aaron is assuming a 3.5% inflation rate between now and retirement age and that any future investments he makes can be compounded at an annual rate of 7% (before taxes).

Aaron has a combined total of $15,000 currently invested in three IRAs that he owns. Assume the same 7% annual growth rate for these funds.

Over the last 3 years, Aaron’s savings rate has averaged 3% of his gross wages.

1.     How much will Aaron need to save each year in order to meet his retirement goal?
   1. Assuming he invests these funds in a non-qualified account?
   2. Assuming he enrolls in and funds his 401(k) to the maximum amount possible?
2. What savings rate does this represent under each of the scenarios above?

The history of Cuba in the last 50 years is noted for its revolution, which brought socialist principles and destroyed the capitalist infrastructure, including the wealth base of its richer inhabitants. From the readings on Cuban history and contemporary society—1) what can be interpreted as the positive social impacts of the revolution on Cuban society (e.g. via race, class, gender); 2) how have the Cuban films we have seen promote the positive impacts of the socialist revolution; and 3) would you say these portrayals are honest reflections of Cuban society or propaganda of the State? Use evidence to back up your assertions.

A stock is currently priced at $110, and the volatility is 32% per annum. Within the next one year, a dividend of $1.5 is expected after two months and again after eight months (Hint: There are two dividends). The risk-free rate of interest is 7% per annum with continuous compounding. Keep four decimal places for all calculations.

2) According to Black’s approximation, what is the value of a 10-month American call with a strike price of $105?

Carbon-14 decays as follows:

_{14 0            14}

                              C   ----> e   + N   

^{6 -1              7}

   isotopic masses are 14.00307 for nitrogen-14 and 14.00324 for carbon-14. What energy change (kJ/moles) occurs in the beta decay of C-14? NOTE: Do I use these two masses to get the mass defect or do I use the mass of protons and nuetrons to find the mass defect of each one and then subtract the two?

Consider the market for a good in which there are two income groups of buyers. There are 8 buyers with income $40 and 6 buyers with income $54. All buyers have the same utility function u = 20q − q 2 + m, where q denotes the amount of the good and m the money left after buying the good. Denote the price of the good by p. (a) [5 points] For each income group, determine the individual demand of a buyer. (b) [5 points] Find the market demand and draw the demand curve. (c) [5 points] Consider an individual buyer in income group $40. For the following prices, determine how much money is left with the buyer after buying the good: (i) p = 8, (ii) p = 13. (d) [5 points] Consider an individual buyer in income group $54. For the following prices, determine how much money is left with the buyer after buying the good: (i) p = 8, (ii) p = 13.

Researchers investigated the speed with which consumers decide to purchase a product. The researchers theorized that consumers with last names that begin with letters later in the alphabet will tend to acquire items faster than those whose last names begin with letters earlier in the alphabet - called the last name effect. MBA students were offered tickets to a basketball game. The first letter of the last name of respondents and their response times were noted. The researchers compared the response times for two​ groups: (1) those with last names beginning with a​ letter, A-​I, and​ (2) those with last names beginning a​ letter, R-Z. Summary statistics for the two groups are provided in the accompanying table. Complete parts a and b below. Sample Size A-I: 18 R-Z: 18 Mean Response Time (Minutes) A-I: 23.26 R-Z: 16.82 Standard Deviation (Minutes) A-I: 9.87 R-Z: 8.49

A. Construct a 90% Confidence Interval for the difference between the true mean response times for MBA students in the two groups.

B. Based on the interval, part A, which group has the shorter mean response time? Does this result support the researchers' last name effect theory? Explain.

This is problem 6-9 from El-Wakil’s Powerplant Technology book -- consider for simplicity an ideal Rankine cycle with turbine inlet and exit steam at 2500 psia and 1000°F, and 1 psia, respectively, and no feedwater heating. The steam mass flow rate is 2x10⁶ lb_m/h. The plant has two-pass surface condenser with 45-ft-long 7/8-in 18-BWG-type 304 stainless steel tubes. Cooling water enters the tubes at 70°F and 7 ft/s. With no flows into the condenser other than turbine steam, find (a) the plant power, in megawatts, and efficiency and (b) the total number of tubes if the condenser terminal temperature difference is 8°F.