Econ 216 - q

ECON 216 BUSINESS STATISTICS MIDTERM EXAMNAME: __________________STUDENT ID: _______

Chapter 6: The Normal Distribution

1) What is the Mean μ and Standard deviation σ of standardized form, the

normal distribution

Answer:

2) Given that X is a normally distributed variable with a mean of 50 and a

standard deviation of 2, find the probability that X is between 47 and 54.

Answer:

3) A company that sells annuities must base the annual payout on the

probability distribution of the length of life of the participants in the plan.

Suppose the probability distribution of the lifetimes of the participants is

approximately a normal distribution with a mean of 68 years and a standard

deviation of 3.5 years.

What proportion of the plan recipients would receive payments beyond age

75?

Answer:






What proportion of the plan recipients die before they reach the standard

retirement age of 65?

Answer:






Find the age at which payments have ceased for approximately 86% of the

plan participants.

Answer:

6) The amount of tea leaves in a can from a particular production line is

normally distributed with μ = 110 grams and σ = 25 grams.

What is the probability that a randomly selected can will contain less than

100 grams or more than 120 grams of tea leaves?

Answer:

PROBABILITY 11/12/13 7:07 AM

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 11/12/13 7:07 AM

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


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


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


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


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


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

City1.30 100

Hudson 1.60 90

Ellswort

h1.80 90

Prescott 2.00 40

Rock

Elm2.40 38

Stillwate

r2.90 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


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



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


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


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


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


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


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


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


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


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


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


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



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


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


regression model, the value of the test statistic is ________.

Answer: 16.2457

Difficulty: Easy

Keywords: F test on the entire regression, test statistic


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


Keywords: interpretation, slope


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


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


Keywords: interpretation, coefficient of multiple determination


A) 14.57% of the total variation in the percentage of students passing the


spending per pupil.

B) 14.57% of the total variation in the percentage of students passing the


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


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

Econ 216 - q

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