Econ 3790           Homework # 1             Dr. Usip

                                    Please Show All Solutions              

Part I: Conceptual Questions, Ch. 1

A. You are paid to investigate the average amount that households in the Greater Youngstown Area spend on grocery in a given quarter of the year.
1
. What is the variable of interest for this study?
2. What is the target population for this study?
3. What is the statistical entity for this study?
4. What is the parameter of interest for this study?
5. How would you make inference about that parameter? Please be specific by listing the relevant statistic and the estimator.
6. Why would you use a random sample for this study?  Please be specific.
7. Will the sample data that you collect be quantitative or qualitative? why?
8. Will the sample data that you collect be time-series or cross-sectional? Why?

B. Do problem # 15, p. 26

Part II: Applications (Use of Excel is Optional), Chs. 2 & 3
A. Refer to problem # 25, p. 28
     Do parts a, b, c, d, only in addition to the following questions:
 e.  From the histogram in part 'd' describe the type of skewness in the distribution of the dataset.
 f. Are there any outliers in the data on gross profit margin? Please show your solutions.
    Hint: Compute the standardized value for the smallest and the largest values in the data.  


B.
Refer to problem # 25, p. 28

For the price/earnings ratio (PER) and gross profit margin (GPM) variables:
1. Use the mean/average to explain the distribution of PER across the companies.
2. Use the median to explain the distribution of PER across the companies..
3. Use the mean/average to explain the distribution of GPM across the companies.
4. Use the median to explain the distribution of GPM across the companies..
5. After looking at the data and the mean values for the two variables an analyst stated that there was less variation (more consistency) in the PER data than in the GPM data. Is this statement true or false? Hint: Use the coefficient of variation to validate your answer
.         

Part III: Probability Problems, Ch. 4
A. Do problem # 8, p. 180, parts 'a', 'b' and following question.  
    
part 'c': What is the probability that both the commission and the council will refuse an application for zoning changes?
 


B. A random sample of 500 respondents in Greater Youngstown Area was selected to study the consumer behavior. Among the questions asked was "Do you enjoy shopping for clothing?" Of the 240 males, 136  answered 'yes'. of the 260 females, 224 answered 'yes'.
1. Complete the contingency table below for use in computing empirical probabilities.

Gender of Respondent                      Response to Question


??

??
?? ??        Totals
?? ?? ??
?? ?? ??
Totals ?? ?? ??

2a. How many joint events are involved in this problem? List them.
2b. How many marginal events are involved in this problem? List them.
3
. What is the probability that a respondent chosen at random
    a. enjoys shopping for clothing?
    b. is a female and enjoys shopping for clothing?
    c.  is a male or a female?
    d. enjoys shopping given that the respondent is a male?
4.
Let A denote the event that a respondent is female and let B denote the event that a respondent enjoys shopping for clothing. Are events A and B independent? Justify with the relevant proof.

Part IV: Expected Value Problem, Ch. 5
A. The table below contains information on the number of daily emergency service calls received by the volunteer ambulance service of Youngstown for the last 50 days: 22 days of which 2 emergency calls  were received, 9 days of which 3 emergency calls were received, 8 days of which no emergency calls were received, etc. 

Number of Service Calls per Day (X) Number of Days (fj)
0 8
1 10
2 22
3 9
4 1
Total 50

1. What is the probability distribution of X?
2. Is this an example of a discrete or continuous probability distribution? Explain.
3. Is this a valid probability distribution? Explain.
4. What is the most likely number of calls that the agency might receive in a given day? 
5. How many calls should the agency expect to receive in a given day?   

B. Nine percent of undergraduate students carry credit card balances greater than $7000 (Reader's Digest, July 2002). Suppose we randomly select 10 students from YSU and interview them about credit card usage.
1. Why is the selection of the 10 students a binomial experiment? Please be specific.
2. What is the probability that two of the students will have a credit card balance greater than $7000?
3. What is the probability that at least three students will have a credit card balance greater than $7000?
4. Consider the outcomes in parts 'b' and 'c', which one is more likely and why?
5. Assuming the total enrollment this semester is 15,000, how many students would you expect to carry credit card balances greater than $7000?


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Last revised: Tuesday, August 29, 2017.