On January 1, 2020 , WXY Inc. replaced the roof on its warehouse. WXY originally built the warehouse and placed it into service on January 1, 1995. The cost of the building was $1,000,000. The building has been depreciated using the straight-line method over an originally estimated 40-year useful life with an estimated salvage value of $50,000. Based on original construction records, WXY is able to calculate that the old roof's cost and accumulated depreciation are 8% of the amounts for the entire building.

The new roof cost $200,000. WXY estimates that the new roof will extend the useful life of the building by 10 years. When the old roof was removed, the old scrap was simply thrown away.

Which of the following statements it true?

On January 1, 2020 , WXY Inc. replaced the roof on its warehouse. WXY originally built the warehouse and placed it into service on January 1, 1995. The cost of the building was $1,000,000. The building has been depreciated using the straight-line method over an originally estimated 40-year useful life with an estimated salvage value of $50,000. Based on original construction records, WXY is able to calculate that the old roof's cost and accumulated depreciation are 8% of the amounts for the entire building.

The new roof cost $200,000. WXY estimates that the new roof will extend the useful life of the building by 10 years. When the old roof was removed, the old scrap was simply thrown away.

Which of the following statements it true?

1. The Bureau of Economic Analysis in the U.S. Department of Commerce reported that the mean annual income for a resident of North Carolina is $ 18,688 with a Standard Deviation of 15000 (USA Today, August 24, 1995). A researcher for the state of South Carolina wants to test the following hypothesis: where μ is the mean annual income for a resident of South Carolina. The researcher gathers information from a sample of 625 residents of South Carolina and finds a sample mean of 17,076 (=17,076) with a sample standard deviation (s) equal to 15,500.

a. What is the appropriate conclusion pertaining to the hypothesis formulated above? Use a .01 level of significance.

b. Construct a 99% Confidence Interval for the value of the mean to mean of the South Carolina residents’ income(assuming you have no knowledge of the population mean and rely solely on the information from your sample).

c. How would your answer to part a change if you did not know the value of the population standard deviation and your sample size was only 25?.

d. What if the researcher was only concerned that the mean income reported by the Bureau might have intentionally exaggerated the mean income for the State? How would your answer to part a will change? Demonstrate.

In all these problems, show the area under the curve to graphically demonstrate your answers.

2. Let’s use the data from the sea ice extent by year. a. Do a t-test to determine if the slope = 0, give null and alternative hypotheses, test statistic, pvalue, decision and interpretation. b. Construct a residual plot vs fitted values. c. Look at a histogram of the residuals. d. Are there any obvious outliers? Find that observation that is the most glaring and find out how many standard deviations it is from the mean. Can this be justified to be removed? e. Are the assumptions for regression met? (Linearity, Constant Standard Deviation and Normality of errors). If not, which one is violated.

data:

Year Extent

1980 9.18

1981 8.86

1982 9.42

1983 9.33

1984 8.56

1985 8.55

1986 9.48

1987 9.05

1988 9.13

1989 8.83

1990 8.48

1991 8.54

1992 9.32

1993 8.79

1994 8.92

1995 7.83

1996 9.16

1997 8.34

1998 8.45

1999 8.6

2000 8.38

2001 8.3

2002 8.16

2003 7.85

2004 7.93

2005 7.35

2006 7.54

2007 6.04

2008 7.35

2009 6.92

2010 6.98

2011 6.46

2012 5.89

2013 7.45

2014 7.23

2015 6.97

2016 6.08

2017 6.77

2018 6.13

2019 5.66

A recent study by the World Bank wished to determine whether there was a relationship between the abundance of natural resources in a country and its long term rate of economic growth. Their study used 65 (n) countries over a long period to 1995. Letting Y be the rate of growth measured as a percentage and X be a measure of natural resource abundance, the following relationship between the two variables was estimated. Standard errors of b_o and b₁ are reported in parentheses under the coefficients for b_o and b₁

To test the significance of the relationship, a 5% level of significance was adopted.

1. State the direction of the alternative hypothesis used to test the statistical significance of the relationship. Type gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box.
2. Use the tables in the textbook to determine the critical value (in absolute terms) to three decimal places.
3. Calculate the test statistic, reporting your answer to two decimal places.
4. Is the null hypothesis rejected for this test? Type yes or no.
5. Disregarding your answer in part 4, if the null hypothesis was not rejected, would there appear to be a linear relationship between resource abundance and economic growth? Type yes or no.

Consider the following Data:

By using the definition and discussing what is relevant to the situation, interpret each of the following for both the coffee and tea data. Also, compare each for coffee and tea. Be sure to include the relevant information (state the value of or, in the case of the distribution, include the graphs) with each component.

1. Mean
2. Median
3. Modal Interval
4. Range
5. IQR
6. Standard Deviation
7. Distribution of histogram and box plot
8. Slope of each linear model
9. Y-intercept of Coffee vs. Tea
10. Correlation coefficient for each linear model
11. Relevant interpolations or extrapolations
12. Correlation type for coffee and tea

Use the R script to answer the following questions: (write down your answers in the R script with ##)

(1). Import FarmSize.csv to Rstudio. Use the correct function to build a linear regression model predicting the average size of a farm by the number of farms; Give the model a name (e.g. FarmSize_Model). Call the model name to inspect the intercept and slope of the regression model. Verify the answers in your manual calculation.

(2). Use the correct function to generate the residuals for the 12 examples in the dataset from the model. Create a residual plot, with x axis as independent variable and y axis as residual.

(3). Use the correct function to inspect SSE, Se and r². Write down the values for these measures. Verify the answers in your manual calculation.

(4). Use the correct function to inspect slope statistic testing result. What is the t value for the slope statistic testing? What is the p value? What is the statistical decision?

Modify this python program to print "Happy Birthday!" if today is the person's birthday. Remember that a person has a birthday every year. It is not likely that a newborn will wonder into a bar the day s/he is born. Your program should print "Happy Birthday!" if today's month and day are the same as the person's birthday. For example, if person is born November 3, 1984 and today is November 3, 2019, then a happy birthday message should print.

The code:

import datetime

from dateutil.relativedelta import relativedelta

today = datetime.date.today()
today



"""from .. import * considered bad form."""

# from datetime import *

"""This is better style."""

from datetime import date

today

type(today)

today.month

today.day

#@title Enter birthday
bday_input = "1995-06-15" #@param {type:"date"}
bday_input = input('Enter your birthday: ')
bday_input

bday_comps = bday_input.split('-')
year = bday_comps[0]
month = bday_comps[1]
day = bday_comps[2]
print(month, day, year)

type(year)

year, month, day = bday_input.split('-')
print(month, day, year)

type(year)

bday = datetime.date(int(year), int(month), int(day))
bday

diff = relativedelta(today, bday)
diff

diff.years

if diff.years >= 21:
  print('Welcome!')
  print('Stamp hand.')
else:
  print('Piss off kid.')
print('Next!')

Use the R script to answer the following questions: (write down your answers in the R script with ##)

(1). Import FarmSize.csv to Rstudio. Use the correct function to build a linear regression model predicting the average size of a farm by the number of farms; Give the model a name (e.g. FarmSize_Model). Call the model name to inspect the intercept and slope of the regression model. Verify the answers in your manual calculation.

(2). Use the correct function to generate the residuals for the 12 examples in the dataset from the model. Create a residual plot, with x axis as independent variable and y axis as residual.

(3). Use the correct function to inspect SSE, Se and r². Write down the values for these measures. Verify the answers in your manual calculation.

(4). Use the correct function to inspect slope statistic testing result. What is the t value for the slope statistic testing? What is the p value? What is the statistical decision?

1. A perfectly competitive industry faces a demand curve given by Q^D= 2515 – 2P. The long-run total cost curve of each firm is given by LTC = 10q -.2q²+.004q³. Derive the long-run equilibrium values of output per firm, market output, price, and the number of firms.
2. You are told that in long-run perfectly competitive equilibrium each firm produces 25 units and that the marginal cost at that level of output is $10. Solve for the long-run equilibrium values of market output, price, and the number of firms. The market demand is given by Q^D= 4000 – 10P.
3. Assume the world market for calcium is perfectly competitive and that all existing producers and potential entrants are identical. Consider the following information about the price of calcium. Between 1990 and 1995, the market price was stable at $2/pound. In the first three months of 1996, the market price doubled reaching $4/pound, where it stayed for the remainder of 1996. Throughout 1997 and 1998, the price declined, eventually reaching $2/pound by the end of 1998. Between 1998 and 2002, the price remained stable at $2/pound. Assume that technology has not changed and that input prices have remained constant over the period. Using words, explain this pricing pattern over the period.