The United States Army recently commissioned a study to assess how deeply a bullet penetrates ceramic body armor. In the study, a cylindrical clay model was layered under an armor vest. A projective was then fired, causing an indentation in the clay. The deepest impression in the clay was measured as an indication of survivability of someone wearing the armor. Here are the data that were observed; measurements (Y , measured in mm) were made using a manually controlled digital caliper. The data are already ordered from low to high.

y <- c(22.4,23.6,24.0,24.9,25.5,25.6,25.8,26.1,26.4,26.7,27.4,27.6,28.3, 29.0,29.1,29.6,29.7,29.8,29.9,30.0,30.4,30.5,30.7,30.7,31.0,31.0, 31.4,31.6,31.7,31.9,31.9,32.0,32.1,32.4,32.5,32.5,32.6,32.9,33.1, 33.3,33.5,33.5,33.5,33.5,33.6,33.6,33.8,33.9,34.1,34.2,34.6,34.6, 35.0,35.2,35.2,35.4,35.4,35.4,35.5,35.7,35.8,36.0,36.0,36.0,36.1, 36.1,36.2,36.4,36.6,37.0,37.4,37.5,37.5,38.0,38.7,38.8,39.8,41.0, 42.0,42.1,44.6,48.3,55.0)

(a) Check the normal assumptions with plots. State clearly why do you use the plots and what does the plot imply.

(b) Construct a 95 percent confidence interval for the population mean µ and interpret your interval. Explain clearly (in words) what µ represents in the context of this problem.

(c) A co-worker of yours looks at your interval in part (a) and says, ”I’m confused. Ninetyfive percent of the measurements above should be in this interval, but far fewer are.” How would you respond to him?

(d) Calculate a 95 percent confidence interval for the population standard deviation σ and interpret your interval. Explain clearly (in words) what σ represents in the context of this problem.

The US Federal Reserve Bank (FED) is considering tightening the money supply now. The United States has an open macro-economy including exports and imports, a market for foreign currency (exchange rates are the price in this market), and international capital mobility. If the FED does restrict the money supply, it will affect investment as it would in a closed economy. But now, adjustments in the foreign currency market occur that induce further changes in aggregate Supply and Demand.

Summarize the majority market adjustments to the new monetary policy. First, explain how a change in the money supply affects aggregate demand(and why). Then explain the second level effects on exchange rates, and the market for goods and services (aggregate supply and demand). Use three supply/demand diagrams, one for the money market, one for the goods and services market, and one for the foreign currency market.

Compared to the closed economy we studied earlier in the semester, are the effects of a change in the money supply larger or smaller when the economy is open (Has trade and floating exchange rates)?

What has been the reaction to Donald Trump's announcement that the United States would withdraw from the Paris Agreement?

Imagine you have recently been elected President of the United States (you are free to assume you are from any party and are free to pursue any policy you think is in the best interest of the country). Your security and military advisors are concerned about China’s growing wealth and military capability. You also have members of congress who want you to change policy towards China because American manufacturing jobs often leave the country and some move to China. Your Commerce Secretary emphasizes that the U.S. trade relationship with China provides consumers with cheap products and that we do sell some products to China, like Boeing commercial jets, which provide American jobs. Your Treasury secretary informs you that because of our trade deficit with China we are dependent on China to finance our budget deficit, and without Chinese money we would have to raise interest rates possibly causing a ecession or worse. Your Secretary of State cautions that China must be handled carefully because no matter what we do China will remain large, powerful country in Asia where we have vital security interests. Everyone is looking to you for the next move. What do you do?

1. The United States began including a chicken pox vaccine as part of its standard panel of childhood vaccines in 1995, and shortly after introduced a shingles vaccine for those over the age of 60. In countries that did not vaccinate against chicken pox (today, relatively few), the shingles vaccine was not necessary. Explain why this is the case. Be sure to use terms on the immune system in your response (e.g. secondary immune response, memory cells).

2. Does Flaviviruses enter the lysogenic cycle or not? Explain.

In the united states, paper currency often comes into contact with cocaine directly, during drug deals or usage, or in counting machines where it wears off from one bill to another. A forensic survey collected fifty $1 bills and measured the cocaine content of the bills. Forty-six of the bills had measurable amounts of cocaine on them. Assume that the sample of bills was a random sample. Please answer the following questions.

1. (a) Suppose that the US Treasury Department claims that 4 out of 5 circulating American 1$ bills contain residues of cocaine. Is there any evidence based on these results that the claim is incorrect? Note: find the p-value using pbinomor dbinom.

2. (b) For the test in (a), is there evidence of incorrectness at level 0.01? Explain, briefly.

3. (c) What sort of error could you be making in (a)? Explain briefly, in the context of the problem.

The Cheesecake Factory Incorporated​ (NASDAQ: CAKE​) operates two bakeries in the United States where it makes over 70 desserts for its own restaurants. In​ addition, the Cheesecake Factory bakeries sell selected desserts to a variety of foodservice operators and​ retailers, including Sam's Club​, Walmart​, Target​, BJ's Wholesale Club​, and Barnes & Noble Cafés. The Cheesecake Factory has accounts receivable on its financial statements. The primary source of its accounts receivable is its sales to bakery customers.

** There is no financial statement to reference**

1. When The Cheesecake Factory ships an order to BJ's Wholesale Club on​ account, The Cheesecake Factory​'s total assets would​ (ignore the cost of sales journal entry for this​ question):

a. increase

b. stay the same

c. decrease

d. unable to determine with the information provided

2. When The Cheesecake Factory ships an order to BJ's Wholesale Club on​ account, The Cheesecake Factory​'s total liabilities would​ (ignore the cost of sales journal entry for this​ question):

a. increase

b. stay the same

c. decrease

d. unable to determine with the information provided

3. When The Cheesecake Factory ships an order to BJ's Wholesale Club on​ account, The Cheesecake Factory​'s total equity would​ (ignore the cost of sales journal entry for this​ question):

a. increase

b. stay the same

c. decrease

d. unable to determine with the information provided

4. When The Cheesecake Factory receives payment for an order it shipped to a wholesale customer last​ month, The Cheesecake Factory​'s total assets​ would:

a. increase

b. stay the same

c. decrease

d. unable to determine with the information provided

Suppose the preliteracy scores of three-year-old students in the United States are normally distributed. Shelia, a preschool teacher, wants to estimate the mean score on preliteracy tests for the population of three-year-olds. She draws a simple random sample of 20 students from her class of three-year-olds and records their preliteracy scores (in points).

80,82,83,85,86,91,91,92,92,93,95,97,99,100,100,103,107,108,111,112

a) Calculate the sample mean, sample standard deviation, and standard error (SE) of the students' scores. Round your answers to four decimal places.
b) Determine the t-critical value (t) and margin of error (m) for a 95% confidence interval. Round your answers to three decimal places.
c) What are the lower and upper limits of a 95% confidence interval? Round your answers to three decimal places.
d) Which is the correct interpretation of the confidence interval:

Shelia is 95% confident that the true population mean is between 91.129 points and 99.571 points.

There is a 95% chance that the true population mean is between 91.129 points and 99.571 points.

Shelia is 95% confident that the true population mean is between 90.842 points and 99.858 points.

There is a 95% chance that the population mean is between 90.842 points and 99.858 points.

Shelia is certain that the true population mean is between 90.842 points and 99.858 points.

Congratulations! You have been appointed an economic policy advisor to the United States. You are told that the economy is significantly below its potential output and that the following will happen next year: World income will fall significantly due to the pandemic, and the price of oil will fall significantly due to lack of economic activities, as well as the availability of alternative and more sustainable energy sources (wind, solar, hydro, nuclear), and the U.S. is an oil exporter, along with shale and natural gas.

a) What kind of policies (under Fiscal policy) might you suggest to the government? Mention three.

b) Consider the economic principle held by Classical economists: The economy always returns to its potential in the long run. What are Keynes’s criticisms of this economic principle?

During the 1950s, both the United States and Soviet government's implemented their own forms of so-called "civil defense," to help their civilian populations respond to the new nuclear threat. Describe the official purpose of these programs, and also address the following questions: 1) Were the civil defense programs actually useful or realistic? Why or why not? 2) If they were not realistic in terms of helping people survive a thermonuclear attack, what purpose did they serve?