Problem Set Policies - Questions and Answers - Statistics Assessment Answer

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Problem1.
Foreachofthefollowingscenarios,discuss(inatmost?vesentences)themainissue(s)withrespect to sampling or reporting bias.
a)
A particular city has 14 architects who own their own ?rm. To select a survey sample, each architect was contacted via telephone by order of appearance in the telephone directory, then the ?rst 8 that agreed to be interviewed formed the sample.
b) The September 1992 issue of Prevention magazine included a women’s health survey; approximately 16,500 women responded to the survey. The May 1993 issue reported on the survey results, claiming that “92% of our readers rated their health as excellent, very good, or good”. 
c) Many scholars and policymakers are interested in estimating the prevalence of mental illness among the homeless population. In one study, the authors sampled homeless persons who received medical attention from a clinic that was part of the Health Care for the Homeless project, resulting in an estimated prevalence of 33%.1 The authors maintain that selection bias is not a serious problem because the clinics are easily accessible to homeless people.
Problem2.
The Dunder Mi?in paper company in Scranton, Pennsylvania sells a variety of o?ce supplies. Two salespeople, Peter and Katrina, are coming up for an evaluation. Their manager has asked you to review Peter and Katrina’s last 120 sales calls and recommend one for a raise. PeterandKatrinaareresponsibleforsellingeitherUSBdrivesorprinterpaper. Peterwassuccessful in 10 out of 20 calls for selling USB drives and in 90 out of 100 calls for selling printer paper. Katrina was successful in 75 out of 100 calls for selling USB drives and 19 out of 20 calls for selling printer paper. You decide to recommend Katrina for a raise. The manager objects, pointing out that Katrina had an overall success rate of 78% and Peter had an overall success rate of 83%. Justify your decision to the manager (and be sure to address their objection)
Problem3.
The following graphs are based on data from the National Center for Health Certi?cates.
a) Describe what you see in the two graphs, with particular focus on the di?erences between the two distributions. 
b) Economists are interested in the possible causes driving the shape of the age distribution in 2016. In a few sentences (each), discuss i. A possible reason behind the discrepancy between the 1980 distribution and the 2016 distribution. ii. A possible reason behind the shape of the age distribution in 2016.
Problem4.
FiveThirtyEight is a data journalism site devoted to applying statistical analysis to a variety of current topics in politics, sports, science, economics, and culture. They recently published a series of articles on gun deaths in America, based on data collected from the Centers for Disease Control and Prevention (and other governmental agencies) on all gun deaths in the United States from 2012 - 2014. The main dataset used for the analysis is available as the gun_deaths data. Each case represents a single gun death. – month: Month of death, coded as a numerical variable taking values 1 - 12. – intent: The underlying cause of death, either Accidental, Homicide, Suicide, or Undetermined. Deaths from legal intervention are coded as homicides. – police: Coded Yes if the death is a result of legal intervention by police and No otherwise. – sex: The sex of the individual who died, either F or M. – age: Age of the individual who died, in years.
– race: Race of the individual who died, either Asian/Pacific Islander, Black, Hispanic, Native American/Native Alaskan, or White. – place: Place of injury, either Home, Residential institution, School/instiution[sic], Sports, Street, Trade/service area, Industrial/construction, Farm, Other specified, or Other unspecified. – education: Educational status of the individual who died, either Less than HS, HS/GED, Some college, or BA+.
 a) Using numerical and graphical summaries, describe and compare the distribution of age (of death) between males and females. 
b) Which underlying cause of death contributes the most toward gun deaths? 
c) Identify the proportion of deaths classi?ed as homicides that involved legal intervention by police.
d) During which season did gun deaths most often occur? Assume that spring is March May, summer is June - August, fall is September - November, and winter is December February. 
e) Of the gun deaths in 2012 among individuals with at least a high school education, what proportion of those individuals were white males? 
f) Compare the proportion of gun deaths due to suicide versus homicide between race/ethnicity groups. In a few sentences, summarize the main ?ndings.
Problem5.
Employment statistics represent an important source of metrics for policymakers to use in gauging the overall health of the economy. In the United States, the government measures unemployment using the Current Population Survey (CPS). This survey collects demographic and employment information each month from about 60,000 occupied households. To be eligible to participate in the survey, individuals must be 15 years of age or older and not in the Armed Forces. One person generally responds for all members of the household; this person is called the “reference person” and usually is the person who owns or rents the housing unit. The CPSData.csv ?le contains data from the September 2016 survey. Descriptions of the relevant variables are as follows: – PeopleInHousehold: number of people in the household, including the respondent – Region: the census region the respondent lives in, either Midwest, Northeast, South, or West – State: the state the respondent lives in, either one of the 50 states or the District of Columbia – Age: age in years of the respondent, where 80 represents individuals ages 80-84, and 85 represents individuals ages 85 and higher – Married: marital status of the respondent, either Divorced, Married, Never Married, Separated, or Widowed – Sex: sex of the respondent, either Female or Male
– Education: highesteducationalleveloftherespondent, either Associate degree, Bachelor’s degree, Doctorate degree, High school, Master’s degree, No high school diploma, Professional degree, or Some college, no degree – Race: race of the respondent, either American Indian, Asian, Black, Multiracial, Pacific Islander, White – Hispanic: coded 1 if the respondent is of Hispanic ethnicity, and 0 otherwise – Citizenship: citizenship status of the respondent, either Citizen, Native, Citizen, Naturalized, or Non-Citizen – EmploymentStatus: employment status of the respondent, either Disabled, Employed, Not in Labor Force, Retired, or Unemployed – Industry: industry of employment, available only if the respondent is employed 
a) Explore the variables Age, Sex, and Race. i. Based on these three variables, write a short paragraph describing the basic demographics of the survey respondents. Reference numerical and graphical summaries as appropriate. ii. Do you notice anything odd about the distribution of Age? Point out what you think is unusual.
b) Describe the distribution of the number of people in a household, referencing appropriate numerical and graphical summaries. 
c) Describe the distribution of citizenship status.
d) The CPS di?erentiates between race and ethnicity. For which races do 15% or more of respondents identify as ethnically Hispanic? 
e) Create a graphical summary that shows the association between age and marital status. Describe what you see and comment on whether it is what you might expect intuitively. f) In the following questions, you will be analyzing respondent data from California. i. Create a subset of the data that includes only respondents from the State of California. How many respondents are in this subset? ii. Of the California respondents with at most a high school degree, what is the percentage who report being unemployed? Of the California respondents with at least an associate’s degree, what is the percentage who report being unemployed? iii. Compare the mean age of California residents who work in the ?nancial industry to the mean age of California residents who work in the leisure and hospitality industry.
Problem6.
This problem uses stock data from Apple Corporation (AAPL) and Microsoft Corporation (MSFT).
a) Run the code in the template to plot Apple’s and Microsoft’s stock prices between 01 January 2018 and 22 July 2019. Describe what you see.
b) Compare the return from holding one share of AAPL for this time period versus one share of MSFT. The return over a period of time is the change in value divided by the original price. 
c)
Compute the standard deviation of daily returns for AAPL and MSFT over this time period. Based on the standard deviation, which stock is less volatile? Volatility refers to the degree of ?uctuation in a stock period over time. 
d) Identify the highest and lowest adjusted closing prices of AAPL during this time period, as well as the dates on which they occurred. Do the same for MSFT. 
e) Both MSFT and AAPL are in the S&P 500 Index, a stock index that measures the stock performance of 500 large publicly-traded companies on the US market. It is a weighted index, such that larger companies contribute more to the index than smaller companies. The two largest components of the index are AAPL and MSFT. Thus, we might expect that the returns of these two companies are highly related.
 i. From a graphical summary, describe your impression of the relationship between daily return for AAPL and daily return for MSFT.
 ii. Calculate an appropriate numerical summary for the relationship observed in part i.
 iii. Interpret the value from part ii. in language accessible to an audience who has not taken a statistics course.

 

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