MOCK EXAM
A. MULTIPLE CHOICE
1) The process of using sample statistics to draw conclusions about true population parameters is
called
A) statistical inference.
B) the scientific method.
C) sampling.
D) descriptive statistics.
2) The estimation of the population average family expenditure on food based on the sample
average expenditure of 1,000 families is an example of
A) descriptive statistics.
B) inferential statistics.
C) a parameter.
D) a statistic.
3) A summary measure that is computed to describe a characteristic from only a sample of the
population is called
A) a parameter.
B) a census.
C) a statistic.
D) the scientific method.
4) Which of the following is most likely a population as opposed to a sample?
A) respondents to a newspaper survey.
B) the first 5 students completing an assignment.
C) every third person to arrive at the bank.
D) registered voters in a county.
5) Which of the following is not an element of descriptive statistical problems?
A) An inference made about the population based on the sample.
B) The population or sample of interest.
C) Tables, graphs, or numerical summary tools.
D) Identification of patterns in the data.
6) Most analysts focus on the cost of tuition as the way to measure the cost of a college
education. But incidentals, such as textbook costs, are rarely considered. A researcher at
Drummand University wishes to estimate the textbook costs of first-year students at Drummand.
To do so, she monitored the textbook cost of 250 first-year students and found that their average
textbook cost was $300 per semester. Identify the population of interest to the researcher.
A) All Drummand University students.
B) All college students.
C) All first-year Drummand University students.
D) The 250 students that were monitored.
7) The chancellor of a major university was concerned about alcohol abuse on her campus and
wanted to find out the proportion of students at her university who visited campus bars on the
weekend before the final exam week. Her assistant took a random sample of 250 students and
computed the portion of students in the sample who visited campus bars on the weekend before
the final exam. The portion of all students at her university who visited campus bars on the
weekend before the final exam week is an example of
A) a statistic.
B) a population.
C) a sample.
D) a parameter.
8) The chancellor of a major university was concerned about alcohol abuse on her campus and
wanted to find out the proportion of students at her university who visited campus bars on the
weekend before the final exam week. Her assistant took a random sample of 250 students. The
portion of students in the sample who visited campus bars on the weekend before the final exam
week is an example of ________.
A) a population.
B) a parameter.
C) a statistic.
D) a sample.
9) Mediterranean fruit flies were discovered in California a few years ago and badly damaged the
oranges grown in that state. Suppose the manager of a large farm wanted to study the impact of
the fruit flies on the orange crops on a daily basis over a 6-week period. On each day a random
sample of orange trees were selected from within a random sample of acres. The daily average
number of damaged oranges per tree and the proportion of trees having damaged oranges were
calculated. In this study, drawing conclusions on any one day about the true population
characteristics based on information obtained from the sample is called ________.
A) descriptive statistics.
B) inferential statistics.
C) a parameter.
D) a statistic.
10) The Commissioner of Health in New York State wanted to study malpractice litigation in
New York. A sample of 31 thousand medical records was drawn from a population of 2.7
million patients who were discharged during the year 2009. The proportion of malpractice claims
filed from the sample of 31 thousand patients is ________.
A) a population.
B) a parameter.
C) a statistic.
D) a sample.
SECTION B. SHORT QUESTIONS AND CALCULATION TASKS
Problem 1. What type of measure scale is being used?
1. High school men soccer players classified by their athletic ability: Superior, Average,
Above average.
ANS:……………………………..
2. Baking temperatures for various main dishes: 350, 400, 325, 250, 300
ANS: ……………………………..
3. The colors of crayons in a 24-crayon box.
ANS: ……………………………..
4. Social security numbers.
ANS: ……………………………..
5. Incomes measured in dollars
ANS: ……………………………..
6. A satisfaction survey of a social website by number:
(1) very satisfied, (2) somewhat satisfied, (3) not satisfied.
ANS: ……………………………..
7.Political outlook: extreme left, left-of-center, right-of-center, extreme right.
ANS: ……………………………..
8. Time of day on an analog watch.
ANS: ……………………………..
9. The distance in miles to the closest grocery store.
ANS: ……………………………..
Problem 2. According to a report in the Washington Post (Sep. 5, 2014), the average age of
viewers of television programs broadcast on CBS, NBC, and ABC is 54 years. Suppose a rival
network (e.g., FOX) executive hypothesizes that the average age of FOX viewers is less than 54.
To test her hypothesis, she samples 200 FOX viewers and determines the age of each.
a. Describe the population.
b. Describe the variable of interest.
c. Describe the sample.
d. Describe the inference.
Problem 3. Cola wars is the popular term for the intense competition between Coca-Cola and
Pepsi displayed in their marketing campaigns. Their campaigns have featured claims
consumer preference based on taste tests. Recently, the Huffington Post (Nov. 11, 2013)
conducted a blind taste test of 9 cola brands that included Coca-Cola and Pepsi. (Pepsi finished 1st
and Coke finished 5th.) Suppose, as part of a Pepsi marketing campaign, 1,000 cola consumers are
given a blind taste test (i.e., a taste test in which the two brand names are disguised). Each
consumer is asked to state a preference for brand A or brand B.
a. Describe the population.
b. Describe the variable of interest.
c. Describe the sample.
d. Describe the inference.
Problem 4. A particular fast-food restaurant chain has 6,289 outlets with drive-through windows.
To attract more customers to its drive-through services, the company is considering offering a 50%
discount to customers who wait more than a specified number of minutes to receive their order.
To help determine what the time limit should be, the company decided to estimate the average
waiting time at a particular drive-through window in Dallas, Texas. For 7 consecutive days, the
worker taking customers’ orders recorded the time that every order was placed. The worker who
handed the order to the customer recorded the time of delivery. In both cases, workers used
synchronized digital clocks that reported the time to the nearest second. At the end of the 7-day
period, 2,109 orders had been timed.
a. Describe the process of interest at the Dallas restaurant.
b. Describe the variable of interest.
c. Describe the sample.
d. Describe the inference of interest.
e. Describe how the reliability of the inference could be measured.
Problem 5
Financial analysts who make forecasts of stock prices and recommendations about whether to buy,
sell, or hold specific securities can be categorized as either “buy-side” analysts or “sell-side”
analysts. A group of Harvard Business School professors compared earnings forecasts of buy-side
and sell-side analysts (Financial Analysts Journal, July/August 2008). Data were collected on
3,526 forecasts made by buy-side analysts and 58,562 forecasts made by sell-side analysts, and
the relative absolute forecast error was determined for each. Frequency distributions for buy-side
and sell-side analysts forecast errors (with the sell-side distribution superimposed over the buyside distribution) are shown in the accompanying figure. Based on the figure, the researchers
concluded “that absolute forecast errors for buy-side analysts have a higher mean and variance
than those for the sell-side analysts.” Do you agree? Explain.
Problem 6: The figure below shows the cumulative percentage polygons (ogives) of meal costs
for center city and metro area restaurants. Discuss the figure.
Problem 7: A manufacturer of industrial wheels suspects that profitable orders are being lost
because of the long time the firm takes to develop price quotes for potential customers. To
investigate this possibility, 50 requests for price quotes were randomly selected from the set of all
quotes made last year, and the processing time (in days) was determined for each quote. Each
quote was classified according to whether the order was “lost” or not (i.e., whether or not the
customer placed an order after receiving a price quote). The following chart shows side-by-side
frequency histograms for these data. Interpret the chart. N denotes the placed orders, while Y
denotes the lost orders.
Problem 8: A random sample of 2,000 students who sat for the Graduate Management
Admission Test (GMAT) is selected. For this sample, the mean GMAT score is x = 540 points
and the standard deviation is s = 100 points. One student from the sample, Kara Smith, had a
GMAT score of x = 440 points. What is Kara’s sample z-score?
Problem 9: At one university, the students are given z-scores at the end of each semester rather
than the traditional GPAs. The mean and standard deviation of all students’ cumulative GPAs, on
which the z-scores are based, are 2.7 and 0.5, respectively.
A. Students with z-scores below −1.6 are put on probation. What is the corresponding probationary
GPA?
B. The president of the university wishes to graduate the top 16% of the students with cum laude
honors and the top 2.5% with summa cum laude honors. Where (approximately) should the limits
be set in terms of z-scores? In terms of GPAs? What assumption, if any, did you make about the
distribution of the GPAs at the university?
Problem 10:
We collect data from a survey on wages, education and experience and estimate the model:
wage   0  1educ   2 exp er  u
where: wage= monthly salary
educ= years of education
exper= years of work experience
The results are presented in Table 1.
Table 1: Regression results for eq. (1)
VARIABLES
Model 1
educ
0.644
(0.0538)
0.0701
(0.0110)
-3.391
(0.767)
exper
Constant
Observations
526
SSR
1612
SSE
5548
Standard errors in parentheses
(i) Test the significance of the coefficients β1
(ii) Compute their 99% confidence intervals of β1.
(iii)Test the hypothesis that β1 =0.5
(iv) Calculate R-squared
(1)