Sample Midterm II - Youngstown State University

Sample Midterm Exam II Econ 3790: Statistics for Business and Economics

Instructor: Yogesh Uppal

You are allowed to use a standard size (8.5*11) cheat sheet and a simple calculator. Please write all the answers with a BALL-POINT PEN or an INK PEN.

Multiple Choice Identify the letter of the choice that best completes the statement or answers the question and write it in the space given next to the question number.

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1. A numerical description of the outcome of an experiment is called a a. descriptive statistic b. probability function c. Variance d. random variable

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2. An experiment consists of making 80 telephone calls in order to sell a particular insurance policy. The random variable in this experiment is a a. discrete random variable b. continuous random variable c. complex random variable d. simplex random variable

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3. An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is a a. discrete random variable b. continuous random variable c. complex random variable d. simplex random variable

4. Which of the following is not a property of a binomial experiment? a. the experiment consists of a sequence of n identical trials b. each outcome can be referred to as a success or a failure c. the probabilities of the two outcomes can change from one trial to the next d. the trials are independent

Exhibit 1.1 The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week. Define the random variable X to be the number of days Pete catches fish.

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5. Refer to Exhibit 1.1. The probability that Pete will catch fish on exactly one day is a. .008 b. .096 c. .104 d. .8

6. Refer to Exhibit 1.1. The probability that Pete will catch fish on one day or less is a. .008 b. .096 c. .104 d. .8

7. Refer to Exhibit 1.1. The expected number of days Pete will catch fish is

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a. .6 b. .8 c. 2.4 d. 3

8. Refer to Exhibit 1.1. The variance of the number of days Pete will catch fish is a. .16 b. .48 c. .8 d. 2.4

Exhibit 1.2 The probability distribution for the number of goals the Lions soccer team makes per game is given below.

Number Of Goals

0 1 2 3 4

Probability 0.05 0.15 0.35 0.30 ........

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9. Refer to Exhibit 1.2. Fill in the probability of 4 goals per game. a. 0.25 b. 0.35 c. 1.2 d. 0.15

____ 10. Refer to Exhibit 1.2. The expected number of goals per game is a. 0 b. 1 c. 2, since it has the highest probability d. 2.35

____ 11. Refer to Exhibit 1.2. The standard deviation of number of goals per game is a. 1.06 b. 2.06 c. 3.06 d. 4.06

____ 12. Refer to Exhibit 1.2. What is the probability that in a given game the Lions will score at least 1 goal? a. 0.20 b. 0.55 c. 1.0 d. 0.95

____ 13. A simple random sample of 100 observations was taken from an infinite population. The sample mean and the standard deviation were determined to be 80 and 12 respectively. The standard error of the mean is a. 1.20 b. 0.12 c. 8.00 d. 0.80

____ 14. A population has a mean of 75 and a standard deviation of 8. A random sample of 800 is selected. The expected value of is a. 8 b. 75 c. 800 d. None of these alternatives is correct.

____ 15. The sample statistic s is the point estimator of a. b. c. d.

Exhibit 1.3 In order to estimate the average time spent on the computer terminals per student at a local university, data were collected for a sample of 81 business students over a one week period. Assume the population standard deviation is 1.8 hours.

____ 16. Refer to Exhibit 1.3. The standard error of the mean is a. 7.50 b. 0.39 c. 2.00 d. 0.20

____ 17. Refer to Exhibit 1.3. If the sample mean is 9 hours, then the 95% confidence interval is a. 7.04 to 110.96 hours b. 7.36 to 10.64 hours c. 7.80 to 10.20 hours d. 8.61 to 9.39 hours

____ 18. A random sample of 1000 people was taken. Four hundred fifty of the people in the sample favored Candidate A. The 95% confidence interval for the true proportion of people who favors Candidate A is a. 0.419 to 0.481 b. 0.40 to 0.50 c. 0.45 to 0.55 d. 1.645 to 1.96

____ 19. A population has a mean of 84 and a standard deviation of 12. A sample of 36 observations will be taken. The probability that the sample mean will be between 80.54 and 88.9 is a. 0.0347 b. 0.7200 c. 0.9511 d. 8.3600

Problem

20. Seventy percent of the students applying to a university are accepted.What is the probability that among the next 10 applicants a. At the most 2 will be accepted? b. Exactly 10 will be accepted?

c. Determine the expected number of acceptances d. Compute the standard deviation.

21. A professor at a local university noted that the grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. DO NOT ROUND YOUR NUMBERS. a. The professor has informed us that 7.93 percent of her students received grades of A. What is the minimum score needed to receive a grade of A? b. Students who made 57.93 or lower on the exam failed the course. What percent of students failed the course? c. If 69.5 percent of the students received grades of C or better, what is the minimum score of those who received C's?

22. A sample of 50 blackout sales showed an average price of $ 1,000 for a 40" LCD TV with a standard deviation of $ 400. Answer the following questions. a. What is the standard error of mean? b. Provide a 99 percent confidence interval for the average price of a TV in the population.

Form A Answer Section

MULTIPLE CHOICE

1. ANS: D 2. ANS: A 3. ANS: B 4. ANS: C 5. ANS: B 6. ANS: C 7. ANS: C 8. ANS: B 9. ANS: D 10. ANS: D 11. ANS: A 12. ANS: D 13. ANS: A 14. ANS: B 15. ANS: B 16. ANS: D 17. ANS: D 18. ANS: A 19. ANS: C

PROBLEM 20. ANS:

a. 0.0016 (0.0000059049 + 0.000137781 + 0.0014467005) b. 0.028 c. 0.103 e. 7 f. 1.45 21. ANS:

a. 88.51 b. 8.53% c. 67.39

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