Practice Test-1
ECO320 Fall 2002
Answer all questions. Test ends sharply at 3.50 p.m.
Multiple choice questions 1 - 7. (5 points each).
1. A statistical study of the effects of interest rates on stock prices is an
example of
(a) theoretical statistics
(b) descriptive statistics
(c) analytical statistics
Answer: c
2. The Bureau of Labor Statistics is interested in the employment status of everybody in the US labor force. The population of interest to the Bureau is:
(a) finite quantitative
(b) finite qualitative
(c) infinite quantitative
(d) infinite qualitative
Answer: b
3. You would like to study the incidence of teenage drunk driving in Albany. Which of the following samples is best suited for the purpose?
(a) a sample of SUNY-Albany
students
(b) a random sample of Albany residents
(c) a sample of SUNY-Albany freshmen and sophomores
(d) a sample of Albany residents aged 16 - 19
Answer: d
4. Are the results of any random sample survey likely to contain error of any kind?
(a) no
(b) not if we select the sample so there is no bias
(c) yes, all samples are subject to sampling error and bias
(d) yes, all samples are subject to sampling error due to chance
Answer: d
5. The following is a sample of the ages of students in a typical SUNY
class:
18 20 21 18 19 20 20 21 19
The mode for the above sample is:
(a) 18
(b) 19
(c) 20
(d) 21
Answer: c
6. The median for the sample from question 5 is:
(a) 18
(b) 19
(c) 20
(d) 21
Answer: c
7. Which of the following is a valid probability distribution?
(a) 
(b) 
(c) 
(d) 
Answer: c
Problems
8. (10 points) A hospital manager wants to know the salary distribution of all 256 doctors employed by the hospital. For this purpose she has collected data on the salaries of the 15 heart and brain surgeons working for the hospital. The data is listed below in Table 1 in ascending order of salary:
Table 1
Name Yearly Salary
Jack Daniel $105,000
Sergei Smirnoff $130,000
Johnnie Walker $135,000
Lisa Teachers $135,000
George Dickel $140,000
Trudy Whitehorse $165,000
Jim Beam $175,000
John Black $185,000
Peter White $215,000
Ana Stolichnaya $300,000
Mary Blood $325,000
Finlandia Johnson $350,000
John Ballantine $375,000
Donna Absolut $380,000
Chivas Regal $410,000
To represent the information in the data in Table 1, the manager has designed the following frequency distribution shown in Table 2 below:
Range (in thousands of $) Number of surgeons
$100 - $170 6
$150 - $220 4
$220 - $290 0
$290 - $360 3
$360 - $430 3
Answer the following 4 questions:
1) Is the manager dealing with a population or a sample? What is the
population of interest?
Answer: The manager is dealing with a sample. The population of interest
consists of the salaries of all 256 doctors working for the hospital.
2) Should she expect error in her results? If yes, what error and why?
Answer: Yes.
(i) Bias: Sample contains only salaries of heart and brain surgeons.
(ii)Sampling error: error due to chance, present in every sample.
3) Is the frequency distribution shown above an accurate representation of
the raw data in Table 1 (i.e. using the rules for constructing a frequency
distribution as guidelines, is there something wrong with the distribution?)
Answer: No. There are overlapping intervals.
4) If you had to represent this frequency distribution graphically
(regardless of possible errors - assume the manager will correct them) what
representation would you use?
Answer: Histogram.
9. (15 points) The CEO of a chain of furniture stores is interested in the frequency distribution of sales in all the 20 stores in the chain. She has only grouped data in the form of the following frequency distribution of the sales and must choose a measure of the "average level of sales":
Sales in $mil Number of stores
$100 - $150 3
$150 - $200 5
$200 - $250 8
$250 - $300 3
$300 and above 1
a) Will she be computing a parameter or a statistic?
Answer: She will be computing a parameter, since the data is for the whole
population.
b) Should she prefer the mean or the median as a measure of the
"average level" of sales? Why?
Answer: She should prefer the median as a measure of the "average
level" of sales because of an open-ended interval.
c) What is the mode of the data in the distribution?
Answer: The mode is $225 million, which is the midpoint of the modal interval.
10. (15 points) Based on previous experience, a used car
salesman has established that he can sell 0, 1, 2, or 3 cars per day, with
equal probability.
(a) Is the number of cars he sells per day a random variable?
Answer: Yes.
(b) If so, what values can this random variable take?
Answer: 0, 1, 2, 3.
(c) If the number of cars he sells per day is a random variable construct a
table showing its probability distribution.
Answer: x P(x)
0 1/4
1 1/4
2 1/4
3 1/4
(d) What is the expected value of the number of cars he can sell per day?
Interpret.
Answer:
It may be interpreted as the average number of cars sold over long-run.
(e) What is the variance of the number of cars he can sell per day? What is
the standard deviation? Interpret.
Answer:
The standard deviation is 1.251/2 = 1.118. It is the "average
size" of deviation of the number of cars sold per day from the mean.
12. (5 points) "If you know that the probability that a normal variable
exceeds a certain number, Q, is 0.10, you can be sure that the probability that
this variable is less than - Q is also 0.10". Do you agree? Why or why
not?
Answer: Yes. I agree. Because the normal distribution is symmetric.
Use the attached normal table to answer the following questions.
12. Find the area under the standard normal curve which lies:
(a) between 0 and 1.82 (5 points):
Answer: 0.4656.
(b) between - 0.48 and 2.01 (5 points):
Answer: 0.1844 + 0.4778 = 0.6622.
13. (10 points) The total sales of a firm next year (in millions of dollars)
is a random variable that is approximately normally distributed with mean 300
and standard deviation 60. Calculate the probability that the value of this
random variable lies between 185 and 265.
Answer: Note that X ~ N(300, 602).
Since (185-300)/60=-1.917 and (265-300)/60=-0.5833. The area which lies between
(-1.917, -0.5833) under the standard normal curve is (0.4726-0.2190) = 0.2356,
which is the desired probability.
I did not supply answers to Question 14, 15, and 16. You can compute yourself using examples worked out in the class.