Fresh!Now! is a chain of grocery stores in the United States with 1921 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.

1. 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).

2. 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)

3. 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 14.2.

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).

A

2010

poll asked people in the United States whether they were satisfied with their financial situation. A total of

338

out of

833

people said they were satisfied. The same question was asked in

2012

, and

304

out of

1156

people said they were satisfied.

Part 1 of 2

Your Answer is correct

(a) Construct a

99.8%

confidence interval for the difference between the proportions of adults who said they were satisfied in

2012

and

2010

. Let

p1

denote the proportion of adults who said they were satisfied in

2010

.Use tables to find the critical value and round the answer to at least three decimal places.

A

99.8%

confidence interval for the difference between the proportions of adults who said they were satisfied in

2012

and

2010

is  

<0.077<−p1p20.209.

Part: 1 / 2

1 of 2 Parts Complete

Part 2 of 2

(b) A sociologist claims that the proportion of people who are satisfied increased from  

2010

to  

2012

by more than

0.22

. Does the confidence interval contradict this claim?

Snow avalanches can be a real problem for travelers in the western United States and Canada. A very common type of avalanche is called the slab avalanche. These have been studied extensively by David McClung, a professor of civil engineering at the University of British Columbia. Suppose slab avalanches studied in a region of Canada had an average thickness of μ = 67 cm. The ski patrol at Vail, Colorado, is studying slab avalanches in its region. A random sample of avalanches in spring gave the following thicknesses (in cm).

59 51 76 38 65 54 49 62 68 55 64 67 63 74 65 79

(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x = cm s = cm

(ii) Assume the slab thickness has an approximately normal distribution. Use a 5% level of significance to test the claim that the mean slab thickness in the Vail region is different from that in the region of Canada.

(a) What is the level of significance?

Snow avalanches can be a real problem for travelers in the western United States and Canada. A very common type of avalanche is called the slab avalanche. These have been studied extensively by David McClung, a professor of civil engineering at the University of British Columbia. Suppose slab avalanches studied in a region of Canada had an average thickness of μ = 68 cm. The ski patrol at Vail, Colorado, is studying slab avalanches in its region. A random sample of avalanches in spring gave the following thicknesses (in cm).

(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

(ii) Assume the slab thickness has an approximately normal distribution. Use a 1% level of significance to test the claim that the mean slab thickness in the Vail region is different from that in the region of Canada.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ = 68; H₁: μ > 68 H₀: μ ≠ 68; H₁: μ = 68     H₀: μ = 68; H₁: μ < 68 H₀: μ < 68; H₁: μ = 68 H₀: μ = 68; H₁: μ ≠ 68

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student's t, since we assume that x has a normal distribution and σ is unknown. The Student's t, since we assume that x has a normal distribution and σ is known.     The standard normal, since we assume that x has a normal distribution and σ is known. The standard normal, since we assume that x has a normal distribution and σ is unknown.

What is the value of the sample test statistic? (Round your answer to three decimal places.)


(c) Estimate the P-value.

P-value > 0.250 0.100 < P-value < 0.250     0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010

A

2010

poll asked people in the United States whether they were satisfied with their financial situation. A total of

338

out of

833

people said they were satisfied. The same question was asked in

2012

, and

304

out of

1156

people said they were satisfied.

Part: 0 / 2

0 of 2 Parts Complete

Part 1 of 2

(a) Construct a

99.8%

confidence interval for the difference between the proportions of adults who said they were satisfied in

2012

and

2010

. Let

p1

denote the proportion of adults who said they were satisfied in

2010

.Use tables to find the critical value and round the answer to at least three decimal places.

Assume that the United States invests in government and corporate securities of Country K. In addition, residents of Country K invest in the United States. Approximately $8 billion worth of investment transactions occur between these two countries each year. The total dollar value of trade transactions per year is about $12 million. This information is expected to also hold in the future.

Because your firm exports goods to Country K, your job as international cash manager requires you to forecast the value of Country K’s currency (the “krank”) with respect to the dollar. Explain how each of the following conditions will affect the value of the krank, holding other things equal. Then, aggregate all of these impacts to develop an overall forecast of the krank’s movement against the dollar.

       a.   The U.S. inflation has suddenly increased substantially, while Country K’s inflation remains low.

       b.   The U.S. interest rates have increased substantially, while Country K’s interest rates remain low. Investors of both countries    are attracted to high interest rates.

       c.   The U.S. income level increased substantially, while Country K’s income level has remained unchanged.

       d.   The U.S. is expected to impose a small tariff on goods imported from Country K.

       e.   Combine all expected impacts to develop an overall forecast.

For years, there have been claims from politicians in the United States that the Chinese actively manipulate their currency, the yuan, keeping its value low against the dollar and other major currencies in order to boost Chinese exports. In November 2015, for example, presidential hopeful Donald Trump claimed that “the wanton manipulation of China’s currency” is “robbing Americans of billions of dollars in capital and millions of jobs.”18 But is this claim true? Would it even be possible for China to manipulate the foreign exchange markets to artificially depress the value of their currency? To answer these questions, one needs to look at the history of exchange rate determination for China and understand something about how the international monetary system actually works.

For most of its history, the Chinese yuan was pegged to the U.S. dollar at a fixed exchange rate. When China started to open up its economy to foreign trade and investment in the 1980s, the yuan was devalued by the Chinese government in order to improve the competitiveness of Chinese exports. Thus, the official yuan/USD pegged exchange rate was increased from 1.50 yuan per U.S. dollar in 1980 to 8.62 yuan per U.S. dollar in 1994. With China’s exports growing and the country running a growing current account trade surplus, pressure began to increase for China to let its currency appreciate. In response, between 1997 and 2005, the exchange rate was fixed at 8.27 yuan per U.S. dollar, which represented a small appreciation. One could argue that during this period, China’s currency was indeed undervalued and that this was the result of government policy.

By the 2000s, China’s growing importance in the global economy and the rise of its export-led economy led to calls for the country to reevaluate its fixed exchange rate policy. In response, in July 2005, the country adopted a managed floating exchange rate system. Under this system, the exchange rate for the yuan was set with reference to a basket of foreign currencies that included the U.S. dollar, the euro, the Japanese yen, and the British pound. The daily exchange rate was allowed to float within a narrow band of 0.3 percent around the central parity. The daily band was extended to 0.5 percent in 2007, 1 percent in 2012, and 2 percent in 2014.

Over time, this managed-float system allowed for the appreciation of the Chinese yuan. For example, against the U.S. dollar, the exchange rate changed from 8.27 yuan per dollar in mid-2005 to 6.0875 yuan per U.S. dollar on July 20, 2015, representing an appreciation of 26 percent. More generally, the effective exchange rate index of the yuan against a basket of more than 60 other currencies increased from 86.3 in July 2005 to 123.8 by early 2016, representing as appreciation of 43 percent. The yuan has appreciated by less than this against the U.S. dollar primarily because the U.S. dollar has also been relatively strong and appreciated against many other currencies over the same time period.

These data suggest that rather than artificially trying to keep its currency undervalued, since July 2005, the Chinese have allowed the yuan to increase in value against other currencies, albeit within the constraints imposed by the managed float. In late 2015, this commitment was put to the test when a slowdown in the rate of growth of the Chinese economy led to an outflow of capital from China, which put downward pressure on the yuan. The Chinese responded by trying to maintain the value of the yuan, using its foreign exchange reserves, which are primarily held in U.S. dollars, to buy yuan on the open market and shore up its value. Reports suggest that China spent $500 billion in 2015 to shore up the value of the yuan and more than $1 trillion in 2016. These actions reduced China’s foreign exchange reserves to $3.011 trillion by January 2017, the lowest level since 2012. China appears to be trying to keep the yuan from depreciating below 7 yuan to the U.S. dollar.

One reason for China to protect the value of the yuan against the dollar: A large number of Chinese companies have dollar-denominated debt. If the yuan falls against the dollar, the price of serving that debt goes up when translated into yuan. This could stress the financials of those companies (possibly pushing some into bankruptcy) and make it more difficult for China to hit the government’s economic growth targets. Another reason: China might want to head off charges from the Trump administration that it continues to keep the value of its currency artificially low.

Please provide a summary of the case, and answer the following questions:

1. What are the benefits that China might gain by allowing the yuan to float freely against other major currencies such as the U.S. dollar and the euro? What are the risks? What do you think they should do?
2. Is there any evidence that the Chinese kept the level of its currency artificially low in the past to boost exports? Is China keeping it artificially low today?
3. What policy stance should the United States and the EU adopt toward China with regard to how it manages the value of its currency?