Statistical economics

1

Eco 302: Assignment 1-Fall-2020: Chapters: 1, 2, 3, 5, 6 & 7: Total 250 points

Due by Midnight (11:59 pm), Sunday, October 11th, 2020

True/False Questions carry 2 points each, Multiple Choices carry 4 points each and the Essay type questions carry 10 points each: total 250 points.

True / False Questions (Type T for true and F for False)

Chapter 1

1 An example of a quantitative variable is the telephone number of a person.

2. An example of a ratio scale variable is the mileage of a car.

3. Credit score is an example of a qualitative variable.

Chapter 2

4. When establishing the classes for a frequency table it is not true that the more classes you use the better your frequency table will be.

5.  The cumulative distribution function is initially increasing and then decreasing towards the end.

6. A Histogram is a graphic that is used to depict quantitative data.

Chapter 3

7. The income distribution is skewed to the right; therefore, the Median Income must be greater than the Mean Income.

8. The sample standard deviation formula does Not make it an unbiased estimator.

9. The mean is said to be less resistant to extreme values.

Chapter 5   10. The probability of an event is a value which must be greater than 0 and less than 1.

11. Two events are independent if the probability of one event is not influenced by whether or not the other event occurs. 12. Mutually exclusive events cannot be independent. 13. A subjective probability is a probability assessment that is based on relative frequency. 14. The probability of an event is the product of the probabilities of the sample space outcomes that correspond to the event. 15. If events A and B are independent, then P(A|B) is always equal to P(A) divided by P(B) .

16. Events that have no sample space outcomes in common and, therefore cannot occur simultaneously are referred to as mutually exclusive events.

Chapter 6 17. The binomial experiment consists of n independent, identical trials, each of which results in either success or failure and the probability of success changes from trial to trial. 18. The variance of the binomial distribution is np(1-p).

19. In a binomial distribution the random variable X is continuous.

Chapter 7 20. The mean and variance are not the same for a standard normal distribution.

21. In a statistical study, the random variable X = 1, if the house is colonial and X = 0 if the house is not colonial, then it can be stated that the random variable is continuous.

22.  For a continuous distribution, P(X ≤ 100) is not the same as P(X<100).

23. The actual weight of hamburger patties is an example of a continuous random variable.

24. The number of defective pencils in a lot of 1000 is an example of a continuous random variable.

25. A continuous random variable may not be normally distributed.

Multiple Choice Questions

Chapters 1 and 2 1. The two types of qualitative variables are:  A. Ordinal and ratio B. Interval and ordinal C. Nominal and ordinal D.  Nominal and interval E.  Interval and ratio

2. Which of the following is a Nominal variable? A.  Bank Account Balance B.  Whether a Person Has a Traffic Violation C.  Daily Sales in a Store D.  Air Temperature E.  Value of Company Stock

3. College entrance exam scores, such as GMAT scores, are an example of a(n) ________________ variable. A. Ordinal B. Ratio C. Nominative D. Interval

4. When we are choosing a random sample and we do not place chosen units back into the population, we are: A. Sampling without Replacement B. Sampling with Replacement C. Using a Systematic Sample D. Using a Voluntary Response Sample

5. When developing a frequency distribution, the class (group), intervals should be  A. Large B. Small

C. Integer

D. Mutually exclusive E. Equal

6. If there are 150 values in a data set, how many classes should be created for a frequency histogram?  A. 5 B. 6 C. 7 D. 8 E. 9

Chapter 3

7. Time to degree has become a "hot" topic with federal legislators. At one state university, it was necessary to do a quick calculation when one of the local congressmen called the president. Twenty students were randomly selected from the most recent graduating class and the number of semesters they were enrolled was calculated as: 7, 8, 10, 11, 8, 6, 10, 9, 9, 8, 13, 12, 8, 11, 11, 14, 8, 7, 10, and 12. What is the variance?  A. 8 B. 2.162 C. 9.5 D. 4.674 E. 21.846

8. If one intends to compare the relative variation between two samples involving two different quantitative variables with different measurement scales, then the most appropriate way is to compare the two samples:  A. Standard deviations B. Variances C. Coefficient of variations D. Ranges E. Interquartile ranges

9. In a statistic class, 10 scores were randomly selected with the following results were obtained: 74, 72, 77, 77, 71, 68, 65, 77, 67, 66 What is the median?  A. 71.5 B. 72.0 C. 77.0 D. 71.0 E. 74.0

Chapter 5 10. Two mutually exclusive events having positive probabilities are ______________ dependent.  A. Always B. Sometimes C. Never 11. If two events are independent, we can _____ their probabilities to determine the probability of Intersection. A. Divide B. Add C. Multiply D. Subtract

12. Events that have no sample space outcomes in common and therefore, cannot occur simultaneously are:  A. Independent B. Mutually Exclusive C. Intersections D. Unions

Chapter 6   13. If p = 0.40 and n = 5, then the corresponding binomial distribution is  A. Right skewed B. Left skewed C. Symmetric D. Bimodal

14. The standard deviation of the binomial distribution is equal to:  A. P B. Np C. Px(1-p)n-x D.  (n)(p)(1-p) E.  15. Which of the following is a valid probability value for a random variable?  A. .2 B. 1.01 C. -.7 D. All of the above 16. Which of the following statements about the binomial distribution is not correct?  A. Each trial results in a success or failure B. Trials are independent of each other C. The probability of success remains constant from trial to trial D.  The experiment consists of n identical trials E.  The random variable of interest is continuous 17. Which one of the following statements is not an assumption of the binomial distribution?  A. Sampling is with replacement B. The experiment consists of n identical trials C. The probability of success remains constant from trial to trial D. Trials are independent of each other E. Each trial results in one of two mutually exclusive outcomes 18. A fair die is rolled 10 times. What is the probability that an odd number (1, 3 or 5) will occur less than 3 times?  A. .0547 B. .1172 C. .1550 D. .7752 E. .8450 

19. In a study conducted for the State Department of Education, 30% of the teachers who left teaching did so because they were laid off. Assume that we randomly select 10 teachers who have recently left their profession. Find the probability that exactly 4 of them were laid off.  A. .3000 B. .2668 C. .2001 D. .0090

Chapter 7 20. The area under the normal curve between Z = 0 and Z = 1 is ________________ the area under the normal curve between Z =1 and Z = 2.  A. Less than B. Greater than C. Equal to D. A, B or C above dependent on the value of the mean E. A, B or C above dependent on the value of the standard deviation 

21. If the random variable X has a mean of µ and a standard deviation , then (X- µ)/ has a mean and standard deviation respectively:  A. µ and σ B.  and s C. 0 and 1 D. 1 and 0 22.  The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams. If we select one box of cereal at random from this population, what is the probability that it will weigh less than 904 grams?  A. .8849 B. .3849 C. .1151 D. .7698 E. .2302

23.  The normal approximation of the binomial distribution is appropriate when:  A. np 10 B. n(1–p) 10 C. np ≤ 10 D. np(1–p) ≤ 10 E. np 10 and n(1–p) 10

24. The mean life of a pair of shoes is 40 months with a standard deviation of 8 months. If the life of the shoes is normally distributed, how many pairs of shoes out of one million will need replacement after 36 months?  A. 500,000 B. 691,500 C. 590,000 D. 308,500 E. 410,000

25.  If the random variable of x is normally distributed, ____% of all possible observed values of x will be within three standard deviations of the mean.  A. 68.26 B. 95.44 C. 99.73 D. 98.50 E. None of the above   Essay Type Questions (2 points each) (Must show your work to get full points)

Chapter 2

1. Consider the following data on distances traveled by 60 people to visit the local amusement park.

distance	freq
1-8	20
9-16	18
17-24	10
25-32	6
33-40	6

Expand and construct the table adding columns for relative frequency and cumulative relative frequency. Then plot Histogram, Frequency Polygon and Ogive Curve (using Excel).

2. Math test anxiety can be found throughout the general population. A study of 150 seniors at a local high school was conducted. The following table was produced from the data. Complete the missing parts.

Score Range	Frequency	Relative Frequency	Cumulative Relative Frequency
Very anxious		0.20
Anxious			0.30
Mildly anxious
Generally relaxed	45
Very relaxed		0.32

3. The following frequency table summarizes the distances in miles of 100 patients from a regional hospital. Distance Frequency

0-2 30

2-4 35

4-6 20

6-8 10

8-10 5 Calculate the sample variance and standard deviation for this data (since it is a case of grouped data- use group or class midpoints in the formula in place of X values, and first calculate the sample mean).

Chapter 5 4. At a college, 60 percent of the students are female and 30 percent of the students receive a grade of C. About 35 percent of the students are male and not C students. Use this contingency table.

Gender\Grade	C	Not C or
Female (F)			0.60
Male (M)		0.35
	0.30

If a randomly selected student is a “Not C” student, what is the probability the student is a female student?

5 A and B are independent events. Moreover, P(A) = 0.4 and P(B) = 0.5. Determine P(A B), that is, P(A or B)

6. In a recent survey of homes in a major Midwestern city, 15% of the homes have a fax machine and 65% have a personal computer. Suppose 10% of the homes with a fax machine also have a personal computer. What is the probability that a home has either a fax machine or a personal computer?

Chapter 6 7. The J.O. Supplies Company buys calculators from a Korean supplier. The probability of a defective calculator is 25%. If 16 calculators are selected at random, what is the probability that less than 4 of the calculators will be defective? 

8. An important part of the customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.45 that troubles in a residential service can be repaired on the same day. For the first 8 troubles reported on a given day, what is the probability that more than 3 troubles will be repaired on the same day? 

Chapter 7 9. Given the length an athlete throws a hammer is a normal random variable with mean 60 feet and standard deviation 3 feet, what is the probability he throws it between 55.5 feet and 64.5 feet? 

10. If x is a binomial random variable where n = 100 and p = 0.3, find the probability that x is greater than or equal to 25 using the normal approximation to the binomial.