FINAL EXAM May 2016
Department of Economics Smith College
INTRODUCTION TO STATISTICS AND ECONOMETRICS: ECO 220 01
ECO 22001期末代考 You leave your office each day at 5pm and the pick up time for the day care is 5:20pm. The time that it takes you to drive
Instructor: Vis Taraz
Exam instructions:
- You have two hours to complete the
· Answer all questions in the space provided. Use the back of the page if necessary.
- Permittedmaterials:
- Calculator
- One page of hand written notes (bothsides) ECO 22001期末代考
- Handout with tables for the normal distribution and thetTdistribution
- The exam has 100 points
- Important note: All hypothesis tests shouldstate:
- 1: the null and alternativehypotheses,
- 2: the value of the teststatistic,
- 3: the rejection region and/or rejectionrule,
- 4: the result of the test and a sentence interpreting your conclusion in English.
1.You are a working mother with a child who goes to day care. ECO 22001期末代考
You leave your office each day at 5pm and the pick up time for the day care is 5:20pm. The time that it takes you to drive to the day care center is a random variable that is normally distributed with a mean of 15 minutes and a standard deviation of 6 minutes. The day care center charges a late fine if you arrive after5:20pm. ECO 22001期末代考
Scenario A: Suppose the day care center charges a flat fine of $5 if you arrive after 5:20pm (and this fine is the same regardless of how late you are).
a.Whatis the probability that on a randomly selected day you will have to pay the fine? (4 points)
b.What is the expected value of the fine for you? Interpret your answer. (4points)
c.Whatis the probability that on a randomly selected work week (lasting 5 days) you will have to pay $15 or more in fines? (6 points) ECO 22001期末代考
(problem continues on the next page)
Scenario B: Suppose that instead of the flat fine, the day care center charges a variable fine that depends on how many minutes late you are. Let y represent the fine (in dollars) and let x represent the number of minutes past 5:20pm you arrive. Suppose that ! = ! !!.!
d.Ifthe day care center uses this rule for fines, what is the probability that on a randomly selected day you will have to pay $10 or more in fines? (6 points)
2.You run a business operating a small commuter airplane that carries 50 passengers. ECO 22001期末代考
From previous data sources, you know that the weight of passengers (including the person and their luggage) averages 190 pounds with a standard deviation of 35 pounds. If you operate a full flight with 50 passengers, what the probability that the total weight of all the passengers and their luggage will exceed 10,000 pounds? (8points)
3.You are a medical researcher studying the effects of cholesterol drugs. You run a study of the effectson cholesterol levels of Lovastatin alone or in combination with Colestipol and you obtain these data:
| Control Group (no drugs) | Lovastatin | Lovastatin +
Colestipol |
|
| Sample Mean | 258 | 191 | 172 |
Cholesterol Level
Sample Standard 23.8 21.2 18.5 ECO 22001期末代考
Deviation
There were sixteen patients in each group. Use the data above to test the null hypothesis that adding Colestipol to Lovastatin has no effect on cholesterol levels, compared to Lovastatin alone. Use a twoTtailed test at the 5% significance level. Clearly write out all four steps of the hypothesis testing process and include a sentence that interprets your conclusion. (12 points)
4.A coin is tossed 4 times. Assume that the coin is fair. ECO 22001期末代考
a.Let A be the event that the number of times the coin comes up heads is exactly 0. What isP(A)?(2 points)
b.Let B be the event that the number of times the coin came up heads is exactly 1. What is P(B)? (2 points)
c.Let C be the event that the first two tosses came up heads. What is P(C)? (2points)
d.LetD be the event that the number of times the coin came up heads is greater than What is P(D)? (2 points)
(continues on the next page)
e.Are the events A and B mutually exclusive? (2points)
f.Are the events B and C mutually exclusive? (2points) ECO 22001期末代考
g.Are the events C and D mutually exclusive? (2points)
h.Compute the probability P(A or D). (3points)
i.Compute the probability P(C or D). (3points)
5.To explain the overall satisfaction of people in a country (satisfaction), thefollowing
models were estimated using data from 184 countries, where the numbers in parentheses below the coefficients represent the standard errors of the coefficients:
where:
- gnipc is gross national income per capita expressed in $1000’s (using 2008 USdollars)
- lifexpecis life expectancy at birth, e., number of years a newborn infant could be expected to live, and
- africa is a dummy variable that takes value 1 if the country is in Africa, and is 0
a.In Model 2, what is the interpretation of the coefficient on the variable africa? (4points)
b.InModel 3, interpret the coefficient on l!”#$%#&×!”#$%!, including what it means that this coefficient is negative. (4 points)
(continues on the next page) ECO 22001期末代考
c.Using Model 3, test whether the impact of gnipc on satisfaction is statistically significantly differentfor African countries, compared to the rest of the Perform a fourTstep hypothesis test using a 95% confidence level and interpret your conclusion. (8 points)
d.Calculate the confidence interval associated with your test in part c. Interpret this confidence interval. (4points)
6.Youread a newspaper article that states that researchers have analyzed data from 10,000 US adults, aged 40T65, ECO 22001期末代考
and found that, controlling for gender, height and age, each additional 30 minutes of exercise per week was associated with a body weight that was 6 pounds lower. The article states that these results are significant at the 99% confidence level.
You may assume that the researchers estimated the following model:
where
- weight is measured inpounds,
- exercise is the number of minutes of exercise perweek,
- femaleis a dummy variable that is equal to 1 if the person is female and is equal to 0 otherwise,
- height is measured in inches,and ECO 22001期末代考
- age is measured in
a.Basedon the information given in the newspaper article, what numerical value did the researchers estimate for !!? (4 points)
b.Let!! be the researcher’s coefficient estimate for !!. Based on the information given in the newspaper article, do we have enough information to say what the value of !”(!!) was and/or what range it was in? If so, state what information we have, and justify your If not, say what additional information we would need to have. (6 points)
(continues on the next page) ECO 22001期末代考
c.A footnote in the article states that the regression had an R2 that was equal to 0.13. Explain the interpretation of this R2. Is this R2 consistent with the statistically significant coefficient on exercise? If yes, explain what these two results imply. If not, explain why this is not consistent. (4points)
d.Fromearlier research, it is known that, amongst people in the 40T65 year old range, older people tend to exercise less and tend to have a higher weight. Suppose that the researchers had not controlled for age in their regression model. How would this have affected their coefficient estimate for !!? (6 points)
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