2. Purchasing a Home in Upstate New York A quantitatively savvy, young couple is interested in

purchasing a home in northern New York. They collected data on 26 houses that had recently sold in

the area. They want to predict the selling price of homes (in thousands of dollars) based on the size

of the home (in square feet).

The regression equation is: Price ̂ = -86.097 + 0.248*Size

Regression Statistics

Multiple R 0.745865819

R Square 0.55631582

Adjusted R Square 0.537828979

Standard Error 162.8663093

Observations 26

              Coefficients StandardError    t Stat              P-value

Intercept -86.097322 82.2443144       -1.0468483      0.30559862

Size      0.24792500 0.04519506       5.48566590     1.22193E-05

a. What is the correlation of the data set? Use the correlation value to help describe the association

shown in the data.

b. Write down the regression equation and then use it to predict the selling price of a home that is

1,742 square feet in size.

c. One home in the data set is 1,400 square feet and costs $187,000, calculate the residual for this

home.

d. What is the slope of the regression line? Interpret the slope in context.

e. If it would make sense, provide a clear interpretation of the intercept of the regression line, in

context. Otherwise, explain why the interpretation does not make sense.

f. What are the degrees of freedom for constructing a confidence interval for, or performing a test

for the effectiveness of the model using slope or correlation?

g. Construct and interpret a 95% confidence interval for the population slope.

h. Use the computer output to do a slope test to determine whether size is an effective linear

predictor of the selling price of recently sold homes. Use a significance level of 5%. Include and

label all six steps of a formal test of hypothesis for regression using slope.

i. We could also use the value of the sample correlation to find a test statistic and p-value to test the

effectiveness of the model. Use the sample correlation, r, to find the test statistic and p-value.

Compare these to the results of part h).

j. What is the R2

for this model? Interpret it in context.

Suppose the scores of a certain high school diploma test follow a normal distribution in the population with a mean of 195 and standard deviation of 30.

1. About ______ percent of the students have a score between 135 and 195.

2. About ______ percent of the students have a score between 225 and 255.

3. The middle 95% of the students have a score between ________  and ________   .

4. Recently class A just had a Math exam, but class B had a Verbal exam.

- Joe in class A has a math score of 160, and all the math scores in class A have a mean of 140 and a standard deviation of 10.

- Eric in class B has a verbal score of 80, and all the verbal scores in class B have a mean of 50 and a standard deviation of 12.

Let’s assume students in classes A and B have very similar academic background, and both classes are hugh classes with lots of students. Then roughly speaking, relative to their respective classmates, who did better in the recent exam, Joe or Eric?

5. A sample consists of 26 scores. What is the degrees of freedom for the sample standard deviation?​

Measures of Disease Frequency (Chapter 2)

In 2009, President Obama launched a nationwide initiative to end homelessness in the U.S. by 2020. The homeless are a vulnerable population with limited access to health care and poor health outcomes. In order to allocate sufficient federal and local resources to eliminate homelessness, U.S. cities conduct an annual survey to estimate the number of homeless persons living within major cities. The City of Boston’s Emergency Shelter Commission (ESC) conducted a survey of homelessness on the night of January 25, 2017. Volunteers counted the number of homeless persons living on the streets, in emergency shelters for individuals or families, in domestic violence programs, in residential mental health or substance abuse programs, transitional housing, and in specialized programs.

1. Which of the following best describes the homeless population in the City of Boston?

a. Dynamic population

b. Fixed population

2. Which of the following describes the homeless population that took part in the ESC survey on January 25^th?

a. Dynamic population

b. Fixed population

3. The 2015 Homeless Census counted 3,456 homeless persons in Boston. The 2016 homeless census counted 3,384 homeless persons in Boston. The size of the population in Boston was 665,984 in 2015 and 673,184 in 2016. From 2015-2016, did the burden of homelessness:

a. Increase

b. Decrease

c. Stay the same (2015: .52%, 2016 0.50%)

d. Cannot determine from this information

4. What do you consider to be the biggest limitation in the homeless survey and why?

a. Time of year (winter)

b. Survey conducted one time annually, not more frequently

c. Survey unlikely captured all homeless persons

d. Survey captures prevalence, not incidence of homelessness

PLEASE SOLVED THIS PROBLEM BY HAND AND IN MINITAB:

The following data are direct solar intensity measurements (watts/m²) on different days at a location in southern Spain: 562, 869, 708, 775, 775, 704, 809, 856, 655, 806, 878, 909, 918, 558, 768, 870, 918, 940, 946, 661, 820, 898, 935, 952, 957, 693, 835, 905, 939, 955, 960, 498, 653, 730, and 753. Calculate the sample mean and sample standard deviation. Prepare a dot diagram of these data. Indicate where the sample mean falls on this diagram. Give a practical interpretation of the sample mean.

Give me a scenario using the probability technique to include the mean, weighted mean, median and mode for populations and samples

A researcher wishes to​ estimate, with 90​% ​confidence, the population proportion of adults who eat fast food four to six times per week. Her estimate must be accurate within 5​% of the population proportion. ​

(a) No preliminary estimate is available. Find the minimum sample size needed. ​

(b) Find the minimum sample size​ needed, using a prior study that found that 40​% of the respondents said they eat fast food four to six times per week. ​

(c) Compare the results from parts​ (a) and​ (b).

Homer is studying the relationship between the average daily temperature and time spent watching television and has collected the data shown in the table. The line of best fit for the data is yˆ=−0.6x+94.5. Assume the line of best fit is significant and there is a strong linear relationship between the variables.

Temperature (Degrees) 40506070 Minutes Watching Television 70655952

(a) According to the line of best fit, what would be the predicted number of minutes spent watching television for an average daily temperature of 39 degrees? Round your answer to two decimal places, as needed.

Provide your answer below:

The predicted number of minutes spent watching television is:

And is the answer:

A: reliable and reasonable

B: unreliable but reasonable

C: unreliable and unreasonable

D: reliable but unreasonable

Let ? ∈ {1, 2} and ? ∈ {3, 4} be independent random variables with PMF-s: ??(1)= 1/2 ??(2)= 1/2 ??(3)= 1/3 ??(4)= 2/3

Answer the following questions

(a) Write down the joint PMF

(b) Calculate?(?+?≤5)and?(? −?≥2) 2 ?2+1

(c) Calculate ?(?? ), ?(? ? ), E ? −2
(d) Calculate the C??(?, ? ), C??(1 − ?, 3? + 2) and V??(2? − ? )

(?*) Calculate C??(??, ?), C??(??, ? + ? ) and V?? ?

What percent of undergraduate enrollment in coed colleges and universities in the United States is male? A random sample of 50 such institutions give the following data (Source: USA Today College Guide).

For this problem, use five classes.

(a) Find the class width.

(b) Make a frequency table showing class limits, class boundaries, midpoints, frequencies, relative frequencies, and cumulative frequencies.

(c) Draw a histogram.

(d) Draw a relative-frequency histogram.

(e) Categorize the basic distribution shape.

(f) Draw an ogive.

This question covers aspects and integration of personal development planning and data analysis skills towards professional engineering competencies for employability.

Consider the data-set shown in Table 2, which is a subset of employment statistics for the UK from between 2009 and 2018. For the dates specified, the data records an estimate of the number of thousands of engineering professionals, and of IT and Telecommunications professionals, classified according to sex.

Table 2 A subset of employment statistics for the UK from 2009 until 2018

Source: https://www.ons.gov.uk/employmentandlabourmarket/peopleinwork/employmentandemployeetypes/datasets/employmentbyoccupationemp04

• Imagine that you have been invited to a job interview where you will be asked to give a presentation to a non-expert audience. In advance of the interview you are sent the data in Table 2.
  • i.By use of appropriate representation identify and show three significant correlations or trends in the data, and suggest reasons for these trends. Include your representation as part of your answer, together with descriptions of the three correlations or trends you have identified.
  • ii.Comment on the reliability of your observations of the trends in the data.

Suppose that each of two investments has a 4% chance of a loss of $10 million, a 2% chance of a loss of $1 million, and a 94% chance of a profit of $1 million. They are independent of each other.
a. What is the VaR for one of the investments when the confidence level is 95%?
b. What is the expected shortfall for one of the investments when the confidence level is 95%?
c. What is the VaR for a portfolio consisting of the two investments when the confidence level is 95%?
d. What is the expected shortfall to a portfolio consisting of the two investments when the confidence level is 95%?
e. Show that in this example VaR does not satisfy the subadditivity condition whereas expected shortfall does.

In the following sentences determine the appropriate sampling A, B, C or D

A --- RANDOM (SIMPLE RANDOM SAMPLING)
B --- SYSTEMATIC
C --- STRATIFIED
D --- Cumulative (CONGLOMERATES)

1- A company is divided by DIRECTIVES, EMPLOYEES, SECRETARIES AND WORKERS. It is wanted to make a study to know the level of satisfaction in relation to the benefits that the company has. The head of human resources decides to take a random sample of each category.

2- A university career has “N” students identified in an easy way, the director wants to see the opinion regarding the enrollment process, decides to start in tenth of the entire list and take the sample every 30 items on the list.

3- A university career has “N” students identified per semester (first semester, second semester, ..., ninth semester in an easy way, the principal wants to see the opinion regarding the enrollment process, decides to select 2 semesters and survey all .

4- A university degree has “N” students identified in an easy way, the principal wants to see the opinion regarding the enrollment process, decides to use a random digit table to obtain the sample.

Using the chart below, create a graph that would be appropriate to display age range statistics. First row (1,2,3,4,5) is the header row and should not be included in your graph.

Instructions: Using the numbers in the above chart, select the appropriate graphic representation to use if the data represented age. Using your graph what conclusions can you reach about the primary age group served? At what age group should resources be focused?

Purchasing agent Angela Rodriguez reported the number of sales calls she received from suppliers on each of the past 14 days. Compute the variance for her daily calls during the 14-day period. Treat the data as a sample.

a. 1.88

b. 1.14

c. 1.67

d. .78

e. 1.31