Business and Eco Statistics (ECO-302-02E)

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

Due by Midnight (11:59 pm), Sunday, March 1st, 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 qualitative variable is the mileage of a car.

3. Credit score is an example of an interval scale variable.

Chapter 2

4. When establishing the classes for a frequency table it is not always 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. The relative frequency is the frequency of a class divided by the total number of classes. 

Chapter 3

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

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

9. The Median is the measure of central tendency that divides a population or sample into two equal parts.

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

11. If events A and B are mutually exclusive, then P(A|B) is always equal to zero.

12. Mutually exclusive events cannot be independent.

13. A classical probability measure 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).

16. Events that have no sample space outcomes in common and, therefore cannot occur simultaneously are referred to as mutually independent 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 standard deviation of a binomial distribution is np(1-p).

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

 
Chapter 7

20. The standard deviation and mean are the same for the 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 ≤ 10) is the same as P(X<10).

23. For a continuous distribution, the exact probability of any particular value is always zero.  

24. For a binomial probability experiment, with n = 60 and p =.2, it is appropriate to use the normal approximation to the binomial distribution without continuity correction.

25. All continuous random variables are normally distributed. 

Multiple Choice Questions (Answer marked with underline and bold face)

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

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

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. Which of the following is a quantitative variable? 
A. The make of a TV
B. The VIN of a car
C. The price of a TV
D. Whether a person is a college graduate
E. The Driver’s License Number

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

C. Mutually exclusive

D. Integer
E. Equal

6. If there are 125 values in a data set, how many classes should be created for a frequency histogram? 
A. 4
B. 5
C. 6
D. 7
E. 8

7. An identification of police officers by rank would represent a(n) ____________ level of measurement. 
A. Nominative
B. Ordinal
C. Interval
D. Ratio

Chapter 3

8. Quality control is an important issue at ACME Company which manufacturers light bulbs. In order to conduct testing of the life hours of their light bulbs, they randomly sampled nine light bulbs and measured how many hours they lasted: 378, 361, 350, 375, 200, 391, 375, 368, and 321. What is the Variance? 
A. 342.43
B. 3424.3
C. 58.5
D. 191
E. 10609

9. When using the Chebyshev’s theorem to obtain the bounds for a 99.73 percent of the values in a population, the interval generally will be ___________ the interval obtained for the same percentage if normal distribution is assumed (empirical rule). 
A. wider than
B. narrower than
C. the same as

10.  According to a survey of the top 10 employers in a major city in the Midwest, a worker spends an average of 413 minutes a day on the job. Suppose the standard deviation is 26.8 minutes and the time spent is approximately a normal distribution. What are the times that approximately 95.45% of all workers will fall? 
A. [387.5 438.5]
B. [386.2 439.8]
C. [372.8 453.2]
D. [359.4 466.6]
E. [332.6 493.4]

11. The company financial officer was interested in the average cost of PCs that had been purchased in the past six months. A random sample of the price of 10 computers was taken with the following results: $3,250, $1,127, $2,995, $3,250, $3,445, $3,449, $1,482, $6,120, $3,009, $4,000 What is the median? 
A. 3447
B. 3213
C. 3445
D. 6120
E. 3250

12 Find the z-score for a IQ test score of 90 when the mean is 100 and the standard deviation is 15. 
A. -0.67
B. 0.77
C. -0.77
D. 0.67
E. -10.00

Chapter 5

13. Two mutually exclusive events having positive probabilities are ______________ dependent. 
A. Sometimes
B. Always
C. Never
14. If events A and B are independent, then the probability of simultaneous occurrence of event A and event B can be found with: 
A. P(A)·P(B)
B. P(A)·P(B|A)
C. P(B)·P(A|B)
D. P(A) + P(B)
E. A, B, and C

15. The _______ of two events X and Y is another event that consists of the sample space outcomes belonging to either event X or event Y or both event X and Y. 
A. Complement
B. Intersection
C. Union
D. Joint
E. Conditional

Chapter 6
 
16. If p = 0.55 and n = 15, then the corresponding binomial distribution is 
A. Right skewed
B. Left skewed
C. Symmetric
D. Bimodal
17. Which of the following is a valid probability value for a random variable? 
A. 1.01
B. 0.29
C. -.75
D. All of the above
E. None of the above
18. 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 random variable of interest is continuous
E.  The experiment consists of n identical trials
19. Which one of the following statements is not an essential assumption of the binomial distribution? 
A.  The experiment consists of n identical trials
B.  The probability of success remains constant from trial to trial
C.  Sampling is with replacement
D. Trials are independent of each other
E. Each trial results in one of two mutually exclusive outcomes
20. A six faced fair die is rolled 10 times. What is the probability that an even number (that is, 2, or 4 or 6) will occur between 2 and 4 times (inclusive)? 
A. .6123
B. 0.0439
C. 0.1172
D. 0.3662
E.0.2051

21.  In a study conducted by UCLA, it was found that 25% of college freshmen support increased military spending. If 6 college freshmen are randomly selected, find the probability that: “fewer than 4 support increased military spending”
A. .0330
B. .7844
C. .9624
D. .9954

Chapter 7

22. The area under the normal curve between Z = 1 and Z = 2 is ________________ the area under the normal curve between Z = 0 and Z = 1. 
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 

23. 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

24.  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 more than 904 grams? 
A. .8849
B. .3849
C. .1151
D. .7698
E. .2302

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 (10 points each)

Chapter 2

1. Consider the following data on distances traveled by 100 people to visit the local park.

distance

freq

1-8

30

9-16

20

17-24

25

25-32

10

33-40

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

2. Math test anxiety can be found throughout the general population. A study of 250 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

0.24

Anxious

0.40

Mildly anxious

Generally relaxed

35

Very relaxed

0.18

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

Frequency

0-4 20

4-8 25

8-12 30

12-16 20

16-24 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, 50 percent of the students are female, and 30 percent of the students receive a grade of C. About 40 percent of the students are male and “not C” students. Use this contingency table.

Gender\Grade

C

Not C or

Female (F)

0.50

Male (M)

0.40

0.30

If a randomly selected student is a C student, what is the probability the student is female?

5 A and B are independent events. Moreover, P(A) = 0.7 and P(B) = 0.3. Determine P(A  B), that is, P(A or B)

6.  In a recent survey of homes in a major Midwestern city, 30% of the homes have a fax machine and 75% have a personal computer. Suppose 15% of the homes have both a fax machine and a personal computer. What is the probability that a randomly selected home does not have a fax machine or does not have a personal computer?

Chapter 6
7. The J.O. Supplies Company buys calculators from a Korean supplier. The probability of a defective calculator is 15%. If 16 calculators are selected at random, what is the probability that more than 5 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 0.40 that troubles in a residential service can be repaired on the same day. For the first 7 troubles reported on a given day, what is the probability that more than 4 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 variance 9, what is the probability he throws it between 55 feet and 65 feet? 

10.  If x is a binomial random variable where n = 100 and p = 0.20, find the probability that x is more than 18 using the normal approximation to the binomial. Check the condition for continuity correction.