Download ECON 216 -EXAM I

ECON 216 BUSINESS STATISTICS
MCLA
NAME: __________________STUDENT ID: _______
EXAM 1_ PART II_50 Points
Organizing and Visualizing Data
TABLE 1
An insurance company evaluates many numerical variables about a person
before deciding on an appropriate rate for automobile insurance. A
representative from a local insurance agency selected a random sample of
insured drivers and recorded, X, the number of claims each made in the last
3 years, with the following results.
X
1
2
3
4
5
f
14
18
12
5
1
1) Referring to Table 1, how many drivers are represented in the sample?
2) Referring to Table 1, how many total claims are represented in the
sample?
3) A type of vertical bar chart in which the categories are plotted in the
descending rank order of the magnitude of their frequencies is called a
TABLE 2
Every spring semester, the School of Business coordinates a luncheon with
local business leaders for graduating seniors, their families, and friends.
Corporate sponsorship pays for the lunches of each of the seniors, but
students have to purchase tickets to cover the cost of lunches served to
guests they bring with them. The following histogram represents the
attendance at the senior luncheon, where X is the number of guests each
graduating senior invited to the luncheon and f is the number of graduating
seniors in each category.
4) Referring to the histogram from Table 2, how many graduating seniors
attended the luncheon?
5) A professor of economics at a small Texas university wanted to determine
what year in school students were taking his tough economics course.
Shown below is a pie chart of the results. What percentage of the class took
the course prior to reaching their senior year?
Numerical Descriptive Measures
Health care issues are receiving much attention in both academic and
political arenas. A sociologist recently conducted a survey of citizens over 60
years of age whose net worth is too high to qualify for Medicaid. The ages of
25 senior citizens were as follows:
TABLE 3:
60 61 62 63 64 65 66 68 68 69 70 73 73
74 75 76 76 81 81 82 86 87 89 90 92
6) Referring to Table 3, calculate the arithmetic Mean, Median, and Mode
age of the senior citizens to the nearest hundredth of a year.
7) The prices of Hamburgers and Fish burgers at MCLA on menu are
posted as follow:
X: Hamburgers Price
$ 8, $ 6, $ 4
Y: Fish Burgers Price
$ 7, $ 5, $ 3
Compute the Mean, Standard Deviation, and Coefficient of Variation
for Hamburgers and Fish Burgers.
PROBABILITY
2/6/2014 5:18:00 PM
Chapter 4 Basic Probability
66) A business venture can result in the following outcomes (with their
corresponding chance of occurring in parentheses): Highly Successful
(10%), Successful (25%), Break Even (25%), Disappointing (20%), and
Highly Disappointing (?). If these are the only outcomes possible for the
business venture, what is the chance that the business venture will be
considered Highly Disappointing?
A) 10%
B) 15%
C) 20%
D) 25%
Answer: C
Difficulty: Easy
Keywords: marginal probability
67) A survey of banks revealed the following distribution for the interest rate
being charged on a home loan (based on a 30-year mortgage with a 10%
down payment).
Interest Rate
3.20%
to
3.29%
3.30%
to
3.39%
3.40%
to
3.49%
3.50%
to
3.59%
3.60%
and
above
Probability
0.12
0.23
0.24
0.35
0.06
If a bank is selected at random from this distribution, what is the chance
that the interest rate charged on a home loan will exceed 3.49%?
A) 0.06
B) 0.41
C) 0.59
D) 1.00
Answer: B
Difficulty: Easy
Keywords: marginal probability, addition rule
TABLE 4-1
Mothers Against Drunk Driving is a very visible group whose main focus is to
educate the public about the harm caused by drunk drivers. A study was
recently done that emphasized the problem we all face with drinking and
driving. Four hundred accidents that occurred on a Saturday night were
analyzed. Two items noted were the number of vehicles involved and
whether alcohol played a role in the accident. The numbers are shown
below:
68) Referring to Table 4-1, what proportion of accidents involved more than
one vehicle?
A) 50/400 or 12.5%
B) 75/400 or 18.75%
C) 275/400 or 68.75%
D) 325/400 or 81.25%
Answer: D
Difficulty: Easy
Keywords: contingency table, empirical classical probability, addition rule
69) Referring to Table 4-1, what proportion of accidents involved alcohol and
a single vehicle?
A) 25/400 or 6.25%
B) 50/400 or 12.5%
C) 195/400 or 48.75%
D) 245/400 or 61.25%
Answer: B
Difficulty: Easy
Keywords: contingency table, empirical classical probability, joint probability
70) Referring to Table 4-1, what proportion of accidents involved alcohol or
a single vehicle?
A) 25/400 or 6.25%
B) 50/400 or 12.5%
C) 195/400 or 48.75%
D) 245/400 or 61.25%
Answer: C
Difficulty: Easy
Keywords: contingency table, empirical classical probability, addition rule
71) Referring to Table 4-1, given alcohol was involved, what proportion of
accidents involved a single vehicle?
A) 50/75 or 66.67%
B) 50/170 or 29.41%
C) 120/170 or 70.59%
D) 120/400 or 30%
Answer: B
Difficulty: Easy
Keywords: contingency table, empirical classical probability, marginal
probability
72) Referring to Table 4-1, given that multiple vehicles were involved, what
proportion of accidents involved alcohol?
A) 120/170 or 70.59%
B) 120/230 or 52.17%
C) 120/325 or 36.92%
D) 120/400 or 30%
Answer: C
Difficulty: Easy
Keywords: contingency table, empirical classical probability, conditional
probability, addition rule
Probability Counting Rules
73) A new model car from Ford Motor Company offers a keyless entry
system that utilizes a four-letter code. How many different possible
combinations are there for the code?
Answer: 456,976
Difficulty: Easy
Keywords: counting rule
74) There are 10 finalists at a national dog show. How many different orders
of finishing can there be for all the 10 finalists?
Answer: 3,628,800
Difficulty: Easy
Keywords: counting rule, permutation
75) There are only 4 empty rooms available in a student dormitory for
eleven new freshmen. Each room is considered unique so that it matters
who is being assigned to which room. How many different ways can those 4
empty rooms be filled, one student per room?
Answer: 7,920
Difficulty: Easy
Keywords: counting rule, permutation
Chapter 5 Discrete Probability Distributions
76) If n = 10 and π = 0.70, then the mean of the binomial distribution is
A) 0.07.
B) 1.45.
C) 7.00.
D) 14.29.
Answer: C
Difficulty: Easy
Keywords: binomial distribution, mean
77) If n = 10 and π = 0.70, then the standard deviation of the binomial
distribution is
A) 0.07.
B) 1.45.
C) 7.00.
D) 14.29.
Answer: B
Difficulty: Easy
Keywords: binomial distribution, standard deviation
TABLE 5-4
The following table contains the probability distribution for X = the number
of traffic accidents reported in a day in Corvallis, Oregon.
X
0
1
2
3
4
5
P(X)
0.10
0.20
0.45
0.15
0.05
0.05
78) Referring to Table 5-4, the mean or expected value of the number of
accidents is ________.
Answer: 2.0
Difficulty: Easy
Keywords: probability distribution, mean
REGRESSION ANALYSIS
2/6/2014 5:18:00 PM
Chapter 13 Simple Linear Regression
1) The Y-intercept (b0) represents the
A) predicted value of Y when X = 0.
B) change in estimated Y per unit change in X.
C) predicted value of Y.
D) variation around the sample regression line.
Answer: A
Difficulty: Easy
Keywords: intercept, interpretation
2) The Y-intercept (b0) represents the
A) estimated average Y when X = 0.
B) change in estimated average Y per unit change in X.
C) predicted value of Y.
D) variation around the sample regression line.
Answer: A
Difficulty: Easy
Keywords: intercept, interpretation
3) The slope (b1) represents
A) predicted value of Y when X = 0.
B) the estimated average change in Y per unit change in X.
C) the predicted value of Y.
D) variation around the line of regression.
Answer: B
Difficulty: Easy
Keywords: slope, interpretation
4) The least squares method minimizes which of the following?
A) SSR
B) SSE
C) SST
D) All of the above.
Answer: B
Difficulty: Difficult
Keywords: least squares, properties
TABLE 13-1
A large national bank charges local companies for using their services. A
bank official reported the results of a regression analysis designed to predict
the bank's charges (Y)—measured in dollars per month—for services
rendered to local companies. One independent variable used to predict
service charges to a company is the company's sales revenue (X)—
measured in millions of dollars. Data for 21 companies who use the bank's
services were used to fit the model:
Yi = β0 + β1Xi + εi
The results of the simple linear regression are provided below.
5) Referring to Table 13-1, interpret the estimate of β0, the Y-intercept of
the line.
A) All companies will be charged at least $2,700 by the bank.
B) There is no practical interpretation since a sales revenue of $0 is a
nonsensical value.
C) About 95% of the observed service charges fall within $2,700 of the least
squares line.
D) For every $1 million increase in sales revenue, we expect a service
charge to decrease $2,700.
Answer: B
Difficulty: Moderate
Keywords: intercept, interpretation
6) Referring to Table 13-1, interpret the estimate of σ, the standard
deviation of the random error term (standard error of the estimate) in the
model.
A) About 95% of the observed service charges fall within $65 of the least
squares line.
B) About 95% of the observed service charges equal their corresponding
predicted values.
C) About 95% of the observed service charges fall within $130 of the least
squares line.
D) For every $1 million increase in sales revenue, we expect a service
charge to increase $65.
Answer: C
Difficulty: Difficult
Keywords: standard error of estimate, interpretation
7) Referring to Table 13-1, interpret the p-value for testing whether
β1exceeds 0.
A) There is sufficient evidence (at the α = 0.05) to conclude that sales
revenue (X) is a useful linear predictor of service charge (Y).
B) There is insufficient evidence (at the α = 0.10) to conclude that sales
revenue (X) is a useful linear predictor of service charge (Y).
C) Sales revenue (X) is a poor predictor of service charge (Y).
D) For every $1 million increase in sales revenue, you expect a service
charge to increase $0.034.
Answer: A
Difficulty: Moderate
Keywords: p-value, interpretation
8) Referring to Table 13-1, a 95% confidence interval for β1 is (15, 30).
Interpret the interval.
A) You are 95% confident that the mean service charge will fall between $15
and $30 per month.
B) You are 95% confident that the sales revenue (X) will increase between
$15 and $30 million for every $1 increase in service charge (Y).
C) You are 95% confident that mean service charge (Y) will increase
between $15 and $30 for every $1 million increase in sales revenue (X).
D) At the α = 0.05 level, there is no evidence of a linear relationship
between service charge (Y) and sales revenue (X).
Answer: C
Difficulty: Moderate
Keywords: confidence interval, interpretation
TABLE 13-2
A candy bar manufacturer is interested in trying to estimate how sales are
influenced by the price of their product. To do this, the company randomly
chooses 6 small cities and offers the candy bar at different prices. Using
candy bar sales as the dependent variable, the company will conduct a
simple linear regression on the data below:
City
Price ($) Sales
River
City
1.30
100
Hudson 1.60
90
Ellswort
1.80
h
90
Prescott 2.00
40
Rock
Elm
2.40
38
Stillwate
2.90
r
32
9) Referring to Table 13-2, what is the estimated slope for the candy bar
price and sales data?
A) 161.386
B) 0.784
C) -3.810
D) -48.193
Answer: D
Difficulty: Moderate
Keywords: slope, estimation
10) Referring to Table 13-2, what is the estimated mean change in the sales
of the candy bar if price goes up by $1.00?
A) 161.386
B) 0.784
C) -3.810
D) -48.193
Answer: D
Difficulty: Moderate
Keywords: slope, interpretation
11) Referring to Table 13-2, what is the coefficient of correlation for these
data?
A) -0.8854
B) -0.7839
C) 0.7839
D) 0.8854
Answer: A
Difficulty: Moderate
Keywords: coefficient of correlation, estimation
12) Referring to Table 13-2, what is the percentage of the total variation in
candy bar sales explained by the regression model?
A) 100%
B) 88.54%
C) 78.39%
D) 48.19%
Answer: C
Difficulty: Moderate
Keywords: coefficient of determination, interpretation
13) Referring to Table 13-2, what percentage of the total variation in candy
bar sales is explained by prices?
A) 100%
B) 88.54%
C) 78.39%
D) 48.19%
Answer: C
Difficulty: Moderate
Keywords: coefficient of determination, interpretation
14) Referring to Table 13-2, what is the standard error of the estimate, SYX,
for the data?
A) 0.784
B) 0.885
C) 12.650
D) 16.299
Answer: D
Difficulty: Moderate
Keywords: standard error of estimate, estimation
15) Referring to Table 13-2, what is the standard error of the regression
slope estimate,
?
A) 0.784
B) 0.885
C) 12.650
D) 16.299
Answer: C
Difficulty: Moderate
Keywords: standard error, slope
16) Referring to Table 13-2, what is
for these data?
A) 0
B) 1.66
C) 2.54
D) 25.66
Answer: B
Difficulty: Moderate
Keywords: sum of squares
17) Referring to Table 13-2, to test that the regression coefficient, β1, is not
equal to 0, what would be the critical values? Use α = 0.05.
A) ±2.5706
B) ±2.7764
C) ±3.1634
D) ±3.4954
Answer: B
Difficulty: Difficult
Keywords: t test on slope, critical value
18) Referring to Table 13-2, to test whether a change in price will have any
impact on sales, what would be the critical values? Use α = 0.05.
A) ±2.5706
B) ±2.7765
C) ±3.1634
D) ±3.4954
Answer: B
Difficulty: Difficult
Keywords: t test on slope, critical value
19) Referring to Table 13-2, if the price of the candy bar is set at $2, the
estimated mean sales will be
A) 30.
B) 65.
C) 90.
D) 100.
Answer: B
Difficulty: Moderate
Keywords: estimation of mean values
20) Referring to Table 13-2, if the price of the candy bar is set at $2, the
predicted sales will be
A) 30.
B) 65.
C) 90.
D) 100.
Answer: B
Difficulty: Moderate
Keywords: prediction of individual values
dard error of estimate, interpretation
EXTRA CREDIT:
Chapter 14 Introduction to Multiple Regression
TABLE 14-10
21) You worked as an intern at We Always Win Car Insurance Company last
summer. You notice that individual car insurance premiums depend very
much on the age of the individual and the number of traffic tickets received
by the individual. You performed a regression analysis in EXCEL and
obtained the following partial information:
22) Referring to Table 14-10, the proportion of the total variability in
insurance premiums that can be explained by AGE and TICKETS is
________.
Answer: 0.7303
Difficulty: Easy
Keywords: coefficient of multiple determination, interpretation
23) Referring to Table 14-10, the proportion of the total variability in
insurance premiums that can be explained by AGE and TICKETS after
adjusting for the number of observations and the number independent
variables is ________.
Answer: 0.6853
Difficulty: Easy
Keywords: adjusted r-square
24) Referring to Table 14-10, the standard error of the estimate is
________.
Answer: 226.7502
Difficulty: Easy
Keywords: standard error of estimate
25) Referring to Table 14-10, the estimated mean change in insurance
premiums for every 2 additional tickets received is ________.
Answer: (243.4401)∗2 = 486.8802
Difficulty: Difficult
Keywords: slope, interpretation
26) Referring to Table 14-10, the 99% confidence interval for the change in
mean insurance premiums of a person who has become 1 year older (i.e.,
the slope coefficient for AGE) is -1.4061 ± ________.
Answer: 7.9382
Difficulty: Moderate
Keywords: slope, interpretation, confidence interval
27) Referring to Table 14-10, the total degrees of freedom that are missing
in the ANOVA table should be ________.
Answer: 14
Difficulty: Easy
Keywords: degrees of freedom
28) Referring to Table 14-10, the regression sum of squares that is missing
in the ANOVA table should be ________.
Answer: 1,670,569.3000
Difficulty: Easy
Keywords: sum of squares
29) Referring to Table 14-10, the residual mean squares (MSE) that are
missing in the ANOVA table should be ________.
Answer: 51,415.6517
Difficulty: Easy
Keywords: mean squares
30) Referring to Table 14-10, to test the significance of the multiple
regression model, what is the form of the null hypothesis?
A) H0 : β1 = 0
B) H0 : β2= 0
C) H0 : β1 = β2 = 0
D) H0 : β0 = β1 = β2 = 0
Answer: C
Difficulty: Easy
Keywords: F test on the entire regression, form of hypothesis
31) Referring to Table 14-10, to test the significance of the multiple
regression model, the value of the test statistic is ________.
Answer: 16.2457
Difficulty: Easy
Keywords: F test on the entire regression, test statistic
32) Referring to Table 14-10, to test the significance of the multiple
regression model, the p-value of the test statistic in the sample is
________.
Answer: 0.0004
Difficulty: Easy
Keywords: F test on the entire regression, p-value
33) To explain personal consumption (CONS) measured in dollars, data is
collected for
INC:
personal income in dollars
CRDTLIM: $1 plus the credit limit in dollars available to the individual
APR:
mean annualized percentage interest rate for borrowing for
the individual
ADVT:
per person advertising expenditure in dollars by
manufacturers in the city where the individual lives
SEX:
gender of the individual; 1 if female, 0 if male
A regression analysis was performed with CONS as the dependent variable
and CRDTLIM, APR, ADVT, and GENDER as the independent variables. The
estimated model was
What is the correct interpretation for the estimated coefficient for GENDER?
A) Holding the effect of the other independent variables constant, mean
personal consumption for females is estimated to be $0.39 higher than
males.
B) Holding the effect of the other independent variables constant, mean
personal consumption for males is estimated to be $0.39 higher than
females.
C) Holding the effect of the other independent variables constant, mean
personal consumption for females is estimated to be 0.39% higher than
males.
D) Holding the effect of the other independent variables constant, mean
personal consumption for males is estimated to be 0.39% higher than
females.
Answer: A
Difficulty: Easy
Keywords: dummy variable, slope, interpretation
TABLE 14-15
The superintendent of a school district wanted to predict the percentage of
students passing a sixth-grade proficiency test. She obtained the data on
percentage of students passing the proficiency test (% Passing), mean
teacher salary in thousands of dollars (Salaries), and instructional spending
per pupil in thousands of dollars (Spending) of 47 schools in the state.
Following is the multiple regression output with Y = % Passing as the
dependent variable, X1 = Salaries and X2 = Spending:
34) Referring to Table 14-15, which of the following is a correct statement?
A) The mean percentage of students passing the proficiency test is
estimated to go up by 2.79% when mean teacher salary increases by one
thousand dollars.
B) The mean teacher salary is estimated to go up by 2.79% when mean
percentage of students passing the proficiency test increases by 1%.
C) The mean percentage of students passing the proficiency test is
estimated to go up by 2.79% when mean teacher salary increases by one
thousand dollars holding constant the instructional spending per pupil.
D) The mean teacher salary is estimated to go up by 2.79% when mean
percentage of students passing the proficiency test increases by 1% holding
constant the instructional spending per pupil.
Answer: C
Difficulty: Moderate
Keywords: interpretation, slope
35) Referring to Table 14-15, which of the following is a correct statement?
A) 18.26% of the total variation in the percentage of students passing the
proficiency test can be explained by mean teacher salary and instructional
spending per pupil.
B) 18.26% of the total variation in the percentage of students passing the
proficiency test can be explained by mean teacher salary and instructional
spending per pupil after adjusting for the number of predictors and sample
size.
C) 18.26% of the total variation in the percentage of students passing the
proficiency test can be explained by mean teacher salary holding constant
the effect of instructional spending per pupil.
D) 18.26% of the total variation in the percentage of students passing the
proficiency test can be explained by instructional spending per pupil holding
constant the effect of mean teacher salary.
Answer: A
Difficulty: Moderate
Keywords: interpretation, coefficient of multiple determination
36) Referring to Table 14-15, which of the following is a correct statement?
A) 14.57% of the total variation in the percentage of students passing the
proficiency test can be explained by mean teacher salary and instructional
spending per pupil.
B) 14.57% of the total variation in the percentage of students passing the
proficiency test can be explained by mean teacher salary and instructional
spending per pupil after adjusting for the number of predictors and sample
size.
C) 14.57% of the total variation in the percentage of students passing the
proficiency test can be explained by mean teacher salary holding constant
the effect of instructional spending per pupil.
D) 14.57% of the total variation in the percentage of students passing the
proficiency test can be explained by instructional spending per pupil holding
constant the effect of mean teacher salary.
Answer: B
Difficulty: Moderate
Keywords: interpretation, adjusted r-square
37) Referring to Table 14-15, what is the standard error of estimate?
Answer: 5.7351 (%)
Difficulty: Easy
Keywords: standard error of estimate
38) Referring to Table 14-15, predict the percentage of students passing the
proficiency test for a school which has a mean teacher salary of 40,000
dollars, and an instructional spending per pupil of 2,000 dollars.
Answer: 39.5127 (%)
Difficulty: Easy
Keywords: prediction of individual values
39) Referring to Table 14-15, estimate the mean percentage of students
passing the proficiency test for all the schools that have a mean teacher
salary of 40,000 dollars, and an instructional spending per pupil of 2,000
dollars.
Answer: 39.5127 (%)
Difficulty: Easy
Keywords: estimation of mean values
40) Referring to Table 14-15, which of the following is the correct null
hypothesis to test whether instructional spending per pupil has any effect on
percentage of students passing the proficiency test, taking into account the
effect of mean teacher salary?
A) H0 : β0 = 0
B) H0 : β1 = 0
C) H0 : β2 = 0
D) H0 : β3 = 0
Answer: C
Difficulty: Easy
Keywords: t test on slope, form of hypothesis