Part 2: t-Procedures

In this part, we will use t-procedures. t-procedures are both confidence intervals and hypothesis tests that

use a t distribution. They are called t-procedures because they rely on a t-test statistic and/or a t-critical

value, so we only need to know the results of a sample in order to perform these procedures for a population

mean.

In Part 2, you will use the data file TempSample00-18.

(THIS IS THE DATA)

YEAR,Month,High Temperature

2000,Jan,45

2000,Jan,48

2001,Jan,49

2003,Jan,62

2003,Jan,53

2004,Jan,42

2004,Jan,47

2005,Jan,40

2005,Jan,47

2006,Jan,48

2006,Jan,47

2007,Jan,51

2007,Jan,34

2007,Jan,47

2009,Jan,50

2011,Jan,35

2012,Jan,44

2013,Jan,38

2013,Jan,53

2013,Jan,42

2014,Jan,58

2014,Jan,47

2014,Jan,44

2015,Jan,52

2016,Jan,44

2017,Jan,49

2018,Jan,54

2000,Feb,48

2001,Feb,47

2004,Feb,47

2007,Feb,51

2008,Feb,51

2008,Feb,55

2011,Feb,45

2014,Feb,37

2014,Feb,54

2014,Feb,58

2015,Feb,54

2017,Feb,52

2017,Feb,44

2017,Feb,45

This includes an SRS of daily temperature highs from January and February from the years 2000-2018

(i.e. "recent" highs). The distribution of "recent" daily high temperatures is approximately Normal.

2.1 Getting Started

2.1.1 Understanding the Set-Up

1) Describe the intended population?

2) Describe the sample?

3) Describe the variable of interest?

4) Describe the parameter of interest (in context)?

5) Describe the statistic of interest (in context)? Give a numerical value along with your description.

Round to two decimal places.

2.1.2 Checking Conditions

1) Check that the conditions for using t-procedures are satisfied. If they are not, discuss whether or not it is reasonable to use t-procedures.

2.2 Confidence Intervals

2.2.1 Motivating Question: Confidence Intervals

In 2.2, we will try to answer the question:

What is the average daily temperature high in Portland, OR for the

months of January and February during 2000-2018?

2.2.2 Confidence Interval

1) What degrees of freedom are needed?

2) What critical value is used to compute a 95% confidence interval?

3) Give the 95% confidence interval. Round to two decimal places.

4) Interpret your 95% confidence interval.

2.2.3 Wrap Up

1) Answer the motivating question in 2.2.1.

2.3 Hypothesis Tests (Tests of Significance)

2.3.1 Motivating Question: Hypothesis Tests

In 2.3, we will try to answer the question:

Is there evidence to suggest that the average daily temperature high in Portland,

OR for the months of January and February during 2000-2018 is different than

the historical average of 48.35◦F?

2.3.2 Hypothesis Test

1) Perform a hypothesis test for α = .01. Be sure to interpret your p-value in context.

2.3.3 Wrap Up

1) Answer the the motivating question in 2.3.1.

2.4 Final Remarks

1) Based on the data found in Part 2, what would you say about the daily high temperature for "recent"

years compared to "historical" years?

A central air conditioning unit was installed on January 1, 2000 at an initial cost of
P650,000 and was expected to have a salvage value of P50,000 after a life of 7 years. a.
What amount of depreciation had accumulated in a sum-of-the-years’-digit method at the
end of 2003? b. Using the declining balance method, determine the depreciation charged
for 2004 and the book value at the end of 2004. c. If the equipment was sold on Jan 1,
2005 for P100,000, what amount of loss would result from this sale if sinking fund method
was being used with interest of 12% per year?

Show a complete and logical solution

Highland, Lowland and Midland are three countries in a continent. The countries engage heavily in trade with each other and have almost identical facilities provided to consumers by both the private sector and public sector. In 2005, Highland had a Nominal bill of its Economy which amounted to 750 million Krona out of which 89% are from traded goods, Midland had a Nominal bill that amounted to 1.4 trillion Dinar out of which 78% are from traded goods and Lowland had a Nominal bill which amounted to 300 million Rand out of which 100% is from traded goods. The following information is given:

E (KRONA|DINAR) = 0.7

E (DINAR|RAND) = 0.495

E (RAND|US DOLLAR) = 1.2

All the above rates are official exchange rates.

Globally, the living standards of all the countries are measured against the living standards in the United States. In order to see that, the BIG MAC Index is used to determine how much the MAC would cost in each of these countries in USD. In Highland, a MAC approximately costs 2 Krona, in Midland, a MAC costs twice as much as in Highlands, In Lowland, a MAC costs around 1.2 Rand and In US, the MAC costs around $6.32.

1. Calculate the Exchange rate of all the currencies per US Dollar at the official rates.
2. Calculate the Nominal GDP and PPP GDP of Highland, Midland and Lowland in US Dollars.
3. What can you conclude from your answers in part B.?
4. In 2006, Highland and Midland jointly invaded Lowland and took over the country. If Highland took 60% of the Nominal GDP and Midland took 40% of the Nominal GDP. What are the percentage increases in their PPP GDP? (Assume all the exchange rates are unchanged)

0981283248l.e

1.Kenia is a small economy somewhere in the Aka Way. The information given in Table 5 is from a recent issue of the Kenia Economic ObserverThere are only 3 goods produced in Kenia.The table below shows the prices and quantities produced of these goods in 2007, 2008, and 2009 as well as other related data. 2008 is the base year for this economy.

a)      Calculate:

(i) The unemployment rate in 2008. Show the formula and workings.(3.5 marks)

(ii) The labor force participation rate in 2009. Show the formula and workings.(2.5 marks)

(iii) GDP deflator 2008. Show the formula and workings.(4.5 marks)

(iv) GDP deflator 2009. Show the formula and workings.          (4.5 marks)

(v) the inflation rate in 2009. Show the formula and workings. (1.5 marks)

Suppose that in a simple economy, only two types of products are produced: computers and automobiles. Sales and price data for these two products for three different years are as shown below:

a)Assuming that all computers and automobiles are final goods, calculate nominal GDP in 2013, 2014 and 2015.    (4.5 marks)

Nominal GDP in 2003:

Nominal GDP in 2004:

Nominal GDP in 2005

b)Calculate real GDP in 2004 and 2005 year using 2003 as the base year. Show the formula.

Thanks for the help really appreciated it Expert!

And now here we are…a Starbucks on nearly every corner. Even Homer Simpson had something to say about this in a recent episode! This is where I need your help. I would like you to perform a thorough analysis of the data involving the number of Starbucks locations. Our investors are interested to know about the rate of growth as well as to understand issues related to forecasting the number of Starbucks locations in the future. And specifically, we are wondering when the number of stores will reach 37,000 locations. You see, there are currently 37,000 McDonald’s restaurants worldwide, and we have set a goal to reach that number by the year 2020. Do you think we can do it?

1. identify the initial value and the growth rate of your exponential model and explain what they mean in context of Starbucks Stores. Put your explanations in a text box.
2. How well does the exponential function compare to the data from the Starbucks Company Time Line? Answer in a short paragraph in a text box.
3. Use your exponential model to predict when Starbucks will match McDonald’s for the number of locations.

Here are the total returns for the S&P500 for the first ten years of this century. Assume you invested $1 in the S&P500 on January 1, 2001. Your first year's return was -11.85%.

Year Return

2001 -11.85%

2002 -21.97%

2003 28.36%

2004 10.74%

2005 4.83%

2006 15.61%

2007 5.48%

2008 -36.55%

2009 26.94%

2010 18.00% 4 points.

Q1. If you invested $1 at the beginning of the time frame [1/1/2001], how much would it be worth five years later? Show work and calculations. 4 points.

Q2. If you invested $1 at the beginning of the time frame [1/1/2001], how much would it be worth ten years later? Show work and calculations. 4 points.

Q3. What was the arithmetic return for the 10-year period? 4 points.

Q4. What was the standard deviation of returns for the 10-year period? 2 points.

Q5. What was the variance of returns for the 10-year period. 2 points.

Q6. If you assumed returns were "normally distributed", what range of returns would you expect for a given year?

Metropolitan Hospital has estimated its average monthly bed needs, N, as:

N=460+5XN=460+5X

where X = time period (months); (January 2002 = 0)

Assume that no new hospital additions are expected in the area in the foreseeable future. The following monthly seasonal adjustment factors have been estimated, using data from the past five years:

Forecast Metropolitan's bed demand for January, April, July, November, and December 2007.

Suppose the following actual and forecast values for June bed demands have been recorded.

What seasonal adjustment factor would you recommend be used in making future June forecasts?

3.4%

5.5%

0.7%

When performing calculations in the following problems, use the numbers in the table as-is. I.e., do NOT convert 8.5985 to 8.5985% (or 0.085985). Just use plain 8.5985.

1. Using the basic market model regression, ,R p = α + β R m + ϵ , what is the beta of this portfolio?

2. For precision, find the portfolio beta using the excess return market model: R p − R f = α + β ∗ ( R m − R f ) + ϵ

[Hint: compute annual excess returns first, then run regression.]

When performing calculations in the following problems, use the numbers in the table as-is. I.e., do NOT convert 8.5985 to 8.5985% (or 0.085985). Just use plain 8.5985.

1.

For precision, find the portfolio beta using the excess return market model: R p − R f = α + β ∗ ( R m − R f ) + ϵ

[Hint: compute annual excess returns first, then run regression.]

2. Using the excess return beta β∗ from the previous problem, what is Jensen's alpha for the portfolio?

You are an original owner of a publicly traded food service company named Smith’s Foods (SF). Your company has been in the high-end restaurant business (HE) for the past ten years. You announced today that the company will be issuing debt today to open a new fast food division (FF). Opening this new division costs $10M today, which you will fund by issuing debt. Revenues from this new division are expected to be $3.5M next year and are projected to grow by 4 percent per year. Costs from this new division are expected to be $2M next year and are projected to grow by 2 percent per year. The life of this project is 15 years. Analyses of other fast food businesses suggest that the beta of a typical fast food division equals 0.70. Assume that the revenues and costs have similar risk. Throughout this problem, assume a risk-free rate of 3 percent and a market risk premium of 6 percent. a) What is the NPV of this new investment? Is the investment worthwhile? (Hint: you will need to use the growing annuity formula twice: once for revenues and once for costs.) A regression of monthly SF excess stock returns on monthly S&P 500 excess returns from the past ten years tells you that the beta of the high-end division equals 1.5. Directly before the investment in the fast food division, SF was an all-equity firm with 1M shares outstanding trading at $25 per share. This represents the value of the high-end division. Assume that the announcement of the new division does not affect the value or beta of the high-end division. b) What is the beta of the firm after the announcement of the new division? The beta of a firm can be calculated as the value-weighted average of the division betas: ?????????? = ????1 ????1 + ????2 ????1 + ????2 ????1 + ????2 ????2 where the value of the new division equals the present value of its future net cash flows (when calculating the value of the fast food division, do not subtract the initial $10M cost, as this was paid for using newly-issued debt). c) Assume that the beta of the new debt (valued at $10M) equals 0.1. What is the beta of the firm’s equity after the announcement of the new division? d) The beta of your firm’s equity was originally 1.5. There are two reasons why the announcement caused the beta of your firm’s equity to slightly change – one reason caused the original beta to decrease while the other caused it to increase. Briefly explain these reasons.