HOMEWORK SETS
FOR
PRINCIPLES OF STATISTICS I
(ECONOMICS 261)
Lewis Karstensson, Ph.D.
Department of Economics
University of Nevada, Las Vegas
2005
INTRODUCTION
This packet contains the Homework Sets for the ten topics covered in this
course.
Each set contains (1) a list the Terms to Know, and (2) a set of
Problems and Interpretation Questions for a given topic.
It is suggested that
you use the pertinent homework exercises, together with the text readings and
lecture notes, to help you prepare for each course Exam.
You should practice
defining the terms accurately, noting examples of each where appropriate, work
through the problems correctly, and interpret the answers correctly with as
much repetition as is necessary to know the material.
The process of learning
statistics is really no different from that of learning many other things: To
learn how to play tennis well, you have to practice playing good tennis; to
learn how to play the piano well, you have to practice on the piano a lot; and
to learn how to do statistical analysis correctly, you have to practice, and
practice, and practice, doing statistical analysis correctly, that is,
learning the language of statistics, working problems, and interpreting
results correctly.
0.1
Course Topics
The principal topics considered in this course are the following:
______________________________________________________________________________
Topic 1:
Introduction to Statistics
1.
2.
3.
The Probabilistic World
Some Beginning Terms
Some Arithmetic Operations
Topic 2:
1.
2.
3.
Topic 3:
1.
2.
3.
4.
Data Presentation
Table Presentations
Graph Presentations
Using Excel, The Chart Wizard, Function Wizard, Histogram Tool
Descriptive Statistics
Measures of Central Tendency
Measures of Variation
Other Measures
The Excel Descriptive Statistics Tool, Correlation Tool
EXAM 1
Topic 4:
1.
2.
3.
Topic 5:
1.
2.
3.
Probability
The Meaning of Probability
Some Probability Terms
Probability Rules and Problems
Probability Distributions
Random Variables and Distributions
The Binomial Distribution
The Normal Distribution
EXAM 2
Topic 6:
1.
2.
3.
Random Samples and their Distributions
Random Sampling Techniques
Sampling Distributions
The Central Limit Theorem
0.2
0.3
Topic 7:
1.
2.
3.
Topic 8:
1.
2.
3.
Estimation
The Process of Estimation
Confidence Intervals
Sample Size Estimation
Hypothesis Testing
The Process of Hypothesis Testing
Hypothesis Test for a Mean
Hypothesis Test for a Proportion
EXAM 3
Topic 9:
1.
2.
3.
Topic 10:
1.
2.
Small Sample Statistics
Student's t-Statistic
Confidence Interval for a Mean
Hypothesis Test for a Mean
Regression Analysis
Simple Regression Analysis
Interpretation of Excel Regression Output
EXAM 4 (Final Exam)
______________________________________________________________________________
TOPIC 1
INTRODUCTION TO STATISTICS
Terms to Know:
Statistics
Descriptive statistics
Inferential statistics
Population
Parameter
Sample
Statistic
Variable
Quantitative variable
Qualitative variable
Continuous variable
Discrete variable
Dummy variable
Problems and Interpretation Questions:
1.
2.
Identify the following notations:
(a)
µ
(b)
2
σ
(c)
σ
Identify the following notations:
_
(a) X
(b)
S
(c)
S
2
3.
A researcher observes that average
basketball, baseball, and football
thousands of current dollars) were
This is an example of what type of
player salaries in professional
in the United States in 1990 (in
$817, $598, and $350, respectively.
statistics?
4.
A researcher is interested in determining the average income for families
in Nye County, Nevada. To accomplish this, she takes a random sample of
400 families from the county and uses the data gathered from these
families to estimate the average income for families in the entire
county. This is an example of what type of statistics?
1.1
1.2
5.
The owner of a fleet of forty taxis in Las Vegas is trying to estimate
his costs for next year's operations. One major cost item is fuel. He
measures the gas mileage for eight taxis. The results (in miles per
gallon of gasoline) are as follows:
18.1, 13.6, 20.1, 17.5, 17.6, 16.8, 19.0, 19.3
6.
7.
8.
(a)
What is the population of interest in this analysis?
(b)
What is an example of a parameter in this case?
(c)
What is the sample in this analysis?
(d)
What is an example of a statistic in this case?
Given:
X = 1, 2, 3, 4.
(a)
ΣX
(b)
ΣX
(c)
Σ(X-2)
(d)
(ΣX)
(e)
Σ(X-2)
Perform the following summations:
2
2
2
Evaluate the following powers:
(a)
2
(b)
2
(c)
2
(d)
2
3
-3
1
0
Find the following factorials:
(a)
4!
(b)
1!
(c)
0!
TOPIC 2
DATA PRESENTATION
Terms to Know:
Frequency distribution
Relative frequency distribution
Cumulative frequency distribution
Contingency table
Histogram
Frequency polygon
Ogive
Stem and leaf display
Line chart
Bar chart
Column chart
Pie chart
Scatter diagram (plot)
Problems and Interpretation Questions:
1.
For practice in data presentation and interpretation, complete the
following Solved Problems in Kazmier: 2.23, 2.28, 2.29, 2.32, 2.34,
and 2.36.
2.1
TOPIC 3
DESCRIPTIVE STATISTICS
Terms to Know:
Measures of central tendency
Arithmetic mean
Weighted mean
Median
Mode
Measures of variation
Range
Variance
Sum of squares
Standard deviation
Coefficient of variation
Z-value
Empirical rule
Chebyshev's theorem
Skewness
Kurtosis
Correlation coefficient
Outlier
Problems and Interpretation Questions:
1.
The number of accidents which occurred during a given month in the 10
manufacturing departments of an industrial plant was:
2, 0, 0, 3, 3, 12, 1, 0, 5, 0
Calculate and interpret the following parameters for this population
data set:
(a)
(b)
(c)
(d)
2.
arithmetic mean.
median.
mode.
range.
(e) sum of squares.
(f) variance.
(g) standard deviation.
The weights of a sample of outgoing packages in a mail room, weighed to
the nearest ounce, are found to be:
21, 18, 30, 12, 14, 17, 28, 10, 16, 25
Calculate and interpret the following statistics for this sample data
set:
(a)
(b)
(c)
(d)
arithmetic mean.
median.
mode.
range.
(e) sum of squares.
(f) variance.
(g) standard deviation.
3.1
3.2
3.
Suppose the profit rates for firms A, B, and C were 10, 12, and 15
percent, respectively. The assets of firm A were $2 billion whereas
those for the other two firms were $1 billion each. Calculate the:
(a) arithmetic mean rate of profit for the firms.
(b) asset weighted mean rate of profit for the firms.
4.
(a) Calculate coefficients of variation for the distributions given in
problems 1 and 2 above.
(b) Based on the standard deviation, which distribution shows the greater
variation?
(c) Which distribution exhibits the greater relative variation?
5.
(a) Transform the data given in problem 1 above into Z-values.
the observation, X = 1.
Interpret
(b) Calculate the mean and standard deviation of the distribution of
Z-values. Interpret the results.
6.
Suppose the Nevada National Bank is reviewing its service charge and
interest policies on checking accounts that it holds. The Bank has found
that the average daily balance on personal checking accounts is normally
distributed around a mean of $850.00 with a standard deviation of
$150.00. Between what two amounts will the average balance fall 95
percent of the time?
7.
Suppose the rates of return last year on the common stocks in a large
portfolio were normally distributed, with a mean of 20 percent and a
standard deviation of 10 percent.
(a) What proportion of the stocks had a return of between 10 percent and
30 percent?
(b) What proportion of the stocks had a positive return?
8.
(a) What proportion of the observations in any type of distribution will
fall within two standard deviations of the mean?
(b) Does this hold for the distribution given in problem 1 above?
Explain.
9.
10.
A firm manufactures metal rods which must be rejected if they are not
between 8.250 and 8.500 inches in diameter. While the shape of the
distribution of rod sizes is not known, a recent sample of rods indicates
a mean diameter of 8.375 inches and a standard deviation of .025 inches.
Estimate the proportion of rods that can be expected to be rejected.
Calculate the Pearson coefficient of skewness for the distribution given
in problem 1 above. Interpret the result.
TOPIC 4
PROBABILITY
Terms to Know:
Probability
Experiment
Event
Classical approach
Relative frequency approach
Subjective approach
Sample space
Elementary events
Mutually exclusive events
Collectively exhaustive events
Composite events
Complementary events
Independent events
Marginal probability
Union probability
Joint probability
Conditional probability
Problems and Interpretation Questions:
1.
The following contingency table gives admitted headcount student
enrollment data for UNLV for the Fall Semester of 2002:
___________________________________________________
Women
Men
________________
Undergraduate
Graduate
10,403
Totals
______
8,231
18,634
3,024
2,028
________________
5,052
______
Totals
13,427
10,259
23,686
___________________________________________________
(a)
Construct a probability matrix for these data.
(b)
What is the probability that a randomly selected student is a woman?
(c)
What is the probability that a randomly selected student is a woman
or undergraduate?
(d)
What is the probability that a randomly selected student is a woman
and undergraduate?
(e)
What is the probability that a randomly selected woman student is
undergraduate?
4.1
4.2
2.
Because of a firm's growth, it is necessary to transfer one of its
employees to one of its branch stores. Three of the nine employees are
women and each of the nine employees is equally qualified for the
transfer. If the person to be transferred is chosen at random, what is
the probability that the transferred person is a woman?
3.
Of 100 students, 24 are economics majors, 18 are computer science majors,
and 8 are majoring in both economics and computer science. If a student
is picked at random, what is the probability that the selected student
will be an economics major or a computer science major or both?
4.
Suppose 30 percent of American adults own stocks, 20 percent own bonds,
and 10 percent own both stocks and bonds. If an investor is one who owns
stocks and/or bonds, what proportion of American adults are investors?
5.
A firm is considering three possible locations for a new factory. The
probability that site A will be selected is 0.30 and the probability that
site B will be selected is 0.20. If only one location will be chosen,
what is the probability that:
(a)
site A or B will be chosen?
(b)
neither site A nor site B will be chosen?
6.
During a given quarter, the probability that GNP will increase, stay the
same, or decrease is estimated to be 0.60, 0.10, and 0.30, respectively.
What is the probability that GNP will either increase or stay the same
during the given quarter?
7.
A company estimates that 30% of the population has seen its commercial
and that if a person sees its commercial there is a 20% probability that
the person will buy its product. What is the probability that a person
chosen at random from the population will have seen the commercial and
bought its product?
8.
If 10% of all light bulbs a company manufactures are defective, the
probability of any one bulb being defective is .10. What is the
probability that two bulbs drawn independently from the company's stock
will be defective?
9.
Suppose the probability that a prospect will make a purchase when he is
contacted by a salesman is 0.40. If a salesman selects two prospects
randomly from a file and makes contact with them, what is the probability
that both prospects will make a purchase?
10.
A store manager is asked to make three different yes-no decisions that
have no relation to each other. Because he is impatient to leave work,
he flips a coin for each decision. If the correct decision in each case
was yes, what is the probability that:
(a)
all decisions were correct?
(b)
none of the decisions were correct?
(c)
two or more of the decisions were correct?
TOPIC 5
PROBABILITY DISTRIBUTIONS
Terms to Know:
Random variable
Discrete random variable
Continuous random variable
Discrete probability distribution
Probability density curve
Expected value
Bernoulli process
Binomial distribution
Normal distribution
Standard normal variable
Standard normal probability distribution
Normal approximation of the binomial distribution
Problems and Interpretation Questions:
1.
Consider the following probability distribution for the discrete random
variable, X:
X
P(X)
_______________________
5
.2
6
.4
7
.3
8
.1
_______________________
2.
3.
(a)
Find the expected value of the random variable.
(b)
Find the standard deviation of the random variable.
Suppose there is a .97 probability that no accident will occur at a
particular power plant during each day; the probability of one accident
is .02; and there is a .01 probability of two accidents.
(a)
Find the expected number of accidents per day.
(b)
Find the standard deviation for the number of accidents.
The Gamma Corporation is equally likely to sell 0, 1, 2, 3, or 4 bicycles
in a day.
(a)
Find the expected number of bicycles sold per day.
(b)
Find the standard deviation for the number of bicycles sold.
5.1
5.2
4.
The arrival of customers during randomly chosen 10-minute intervals at a
drive-in facility specializing in photo development and film sales has
the following discrete probability distribution:
Arrivals
Probability
X
P(X)
______________________________
0
0.15
1
0.25
2
0.25
3
0.20
4
0.10
5
0.05
______________________________
5.
6.
7.
8.
(a)
Find the expected value of arrivals.
(b)
Find the standard deviation for the arrivals.
Solve the following problems using the binomial formula:
(a)
P(x=4*n=8, p=0.30)
(b)
P(x<2*n=5, p=0.50)
Solve the following problems using the binomial table:
(a)
P(x=4*n=8, p=0.30)
(b)
P(x<2*n=5, p=0.50)
Mary Johnson owns stock in five companies. There is a 0.50 probability
that each stock will rise in price this year.
(a)
Construct a probability distribution for the number of rising stocks
from the binomial table.
(b)
Draw a probability histogram for this distribution.
(c)
Calculate the (1) expected value, (2) variance, and (3) standard
deviation for this distribution.
(d)
What is the probability that all five stocks will increase in price?
(e)
What is the probability that none of the stocks will increase in
price?
(f)
What is the probability that at least two of the stocks will
increase in price?
Suppose that 40 percent of the hourly employees in a large firm are in
favor of union representation, and a random sample of 10 employees are
contacted and asked for an anonymous response. What is the probability
that a majority of the respondents will be in favor of union
representation?
5.3
9.
10.
11.
12.
13.
14.
The Maroni Corporation bids on 10 jobs, believing that its chances of
getting each one is 0.10. What is the probability that the firm will get
one or more of the bids?
Find the area under the standard normal curve which lies between the
Z-values of:
(a)
0 and 1.82
(b)
-1.32 and 0
(c)
-1.08 and 1.08
(d)
-1.32 and -1.46
Find the probability that the standard normal variable, Z, lies:
(a)
above 2.3
(b)
below -3.0
(c)
between 1 and 2
(d)
between -1 and 2
Find the value of Z if the area under the standard normal curve:
(a)
between 0 and Z is .1985
(b)
between -Z and 0 is .0910
(c)
to the left of Z is .8051
(d)
between -Z and Z is .1820
Suppose the annual sales of a given firm is a normally distributed random
variable with a mean of $300 billion and a standard deviation of $60
billion. What is the probability that the sales for this firm for the
year will:
(a)
be less than $280 billion?
(b)
exceed $350 billion?
(c)
be between $185 billion and $265 billion?
(d)
be between $305 billion and $375 billion?
The amount of time required for a given type of automobile transmission
repair at a service garage is normally distributed with a mean of 45
minutes and a standard deviation of 8.0 minutes. The service manager
plans to have work begin on the transmission of a customer's car 10
minutes after the car is dropped off, and he tells the customer that the
car will be ready within 1 hour total time. What is the probability that
he will be wrong?
5.4
15.
16.
Suppose wage increases in a given industry are normally distributed
around a mean increase of $1.00 per hour with a standard deviation of
$0.30 per hour. While union negotiators are now asking for a raise of
$1.45 per hour, they expect to get something less than their request.
They, however, do hope to get a raise of no less than $0.90 per hour.
What is the probability that the wage increase will:
(a)
be more than $1.45 per hour?
(b)
fall within the interval between $0.90 and $1.45?
(c)
be less than $0.90 per hour?
A factory's rate of electric power consumption per day is normally
distributed with a mean consumption rate of 8,000 kilowatts and a
standard deviation of 1,000 kilowatts. What is the probability that the
power consumption on any given day will be:
(a)
at least 6,500 kilowatts?
(b)
greater than 10,000 kilowatts?
17.
New MBA students at UNLV must take the GMAT examination. Suppose the
scores achieved by incoming students are normally distributed with a mean
of 500 and a standard deviation of 50. If UNLV gives a scholarship to
the top 15 percent of the students, what score must be achieved in order
to get a scholarship?
18.
A Myrtle Beach resort hotel has 120 rooms. Hotel room occupancy is
approximately 75%. What is the probability that:
(a)
at least half the rooms are occupied on a given day?
(b)
100 or more rooms are occupied on a given day?
(c)
80 or fewer rooms are occupied on a given day?
TOPIC 6
RANDOM SAMPLES AND THEIR DISTRIBUTIONS
Terms to Know:
Random Sample
Simple random sample
Systematic random sample
Stratified random sample
Cluster (area) sample
Sampling error
Sampling distribution of sample means
Sampling distribution of sample proportions
Central limit theorem
Standard error of the mean
Standard error of the proportion
Problems and Interpretation Questions:
1.
A national tire manufacturer claims that the average lifetime of their
premium tire is 50,000 miles. The standard deviation of the lifetime of
these tires is 2,000 miles. Suppose all possible samples of size 100
are taken from this population of tires. Calculate the standard error of
the mean for this sampling distribution. What does your answer mean?
2.
A local firm claims that their tires last 45,000 miles on average with a
standard deviation of 2,500 miles. Assuming the firm's claim is correct,
suppose a random sample of 100 of these tires is tested. What is the
probability that the sample mean found in the test will be equal to or
less than 44,500 miles?
3.
Studies have shown that the total number of points scored by both teams
in National Football League (NFL) games over several seasons has a mean
of 41 points with a standard deviation of 14 points. What is the
probability of obtaining a mean total score equal to or less than 48
points in a random sample of 30 NFL games?
4.
The family income distribution in St. Paul, Minnesota, is skewed to the
right. The latest census reveals that the mean family income is $32,000
and that the standard deviation is $4,000. If a simple random sample of
75 families is drawn, what is the probability that the sample mean family
income will differ from St. Paul's mean income by more than $500?
5.
It is estimated that there are 1,400 automobile dealers in the Chicago
area and that the average dollar sales per dealer per month is $750,000.
A random sample of 50 dealers is selected, and the mean and standard
deviation are calculated. If the standard deviation is equal to $95,000,
what is the probability that the sample mean is between $740,000 and
$765,000?
6.1
6.2
6.
A recent survey suggests that the average annual starting salary for
economists with a bachelors degree is $34,000 with a standard deviation
of $2,500. If a sample of 50 first-year economists is selected randomly,
what is the probability that the mean starting salary for this sample
will be at least $33,500?
7.
Sears claims that seven percent of all video games purchased during the
Christmas season are defective and returned. Suppose all possible
samples of size 100 are taken from Sears inventory of video games and
tested for defects. Calculate the standard error of the proportion for
this sampling distribution. What does your answer mean?
8.
The unemployment rate in the New Orleans area for a recent month was
9.6%. What is the probability that the percentage unemployed in a random
sample of 600 people is over 10%?
9.
A mortgage company knows that 8% of its home loan recipients default
within the first five years. What is the probability that out of 350
loan recipients, less than 25 will default within the next five years?
10.
From past experience, a company knows that 55 percent of the surveys
that they send out will be completed and returned. What is the
probability that they will have at least 50 percent returned of 125
surveys mailed?
TOPIC 7
ESTIMATION
Terms to Know:
Estimation
Estimator
Estimate
Point estimate
Interval estimate
Confidence coefficient
Sample size estimation
Problems and Interpretation Questions:
1.
For a large bank having several thousand customers, five checking account
balances, selected at random, are: $400, $850, $180, $240, and $160.
What is the point estimate for the mean (F) of all checking account
balances for this bank?
2.
In a survey of 224 large companies conducted by the Conference Board, 45
companies said they give three to five months notice of plant closings.
What is the point estimate of the population proportion (π) of companies
that give such notice of plant closings?
3.
A nursery sells trees of different types and heights. Suppose that 75
pine trees are sold for planting at City Hall. These 75 trees average 60
inches in height with a standard deviation of 16 inches. Calculate the
standard error of the mean for this sample.
4.
Suppose the population standard deviation on the weight of aluminum
ingots is known to be 20 pounds. A random sample of 100 ingots at a
given aluminum plant yielded a mean weight of 602 pounds. Construct a
95 percent confidence interval for the population mean weight of aluminum
ingots.
5.
An economist wishes to estimate the mean population elasticity of supply
of poultry farmers at their respective production levels. A random
sample of 100 producers yields an average elasticity of supply of 1.9
and a standard deviation of 1.0. Construct a 90 percent confidence
interval for the population mean elasticity of supply.
6.
Fifty cans of dog food were randomly sampled for cereal content. The
mean cereal content was 6.0 oz. with a standard deviation of .05 oz.
Construct a 99 percent confidence interval for the population mean cereal
content.
7.
A sample of 100 new home owners were asked if they were satisfied with
the services provided by their real estate agents. In this sample, 92
reported that they were satisfied. Calculate the standard error of
proportion for this sample.
7.1
7.2
8.
A breakfast food company wants to estimate the proportion of cornflake
eaters who prefer the flakes soggy when eaten. A sample of 100 cornflake
eaters reveals that 30 prefer soggy flakes. Construct a 90 percent
confidence interval for the proportion of cornflake eaters in the
population who like soggy flakes.
9.
A survey was taken from a random group of employees of a large firm.
These employees were asked whether or not they were happy with their
jobs. Of the 150 employees surveyed, 90 said they were content with
their current jobs. Calculate a 95 percent confidence interval for the
proportion of employees who were happy with their jobs.
10.
A prospective purchaser wishes to estimate the mean dollar amount of
sales per customer at a toy store located at an airline terminal. Based
on data from other similar airports, the standard deviation of such sales
amounts is estimated to be about $3.20. What size random sample should
she collect, as a minimum, if she wants to estimate the mean sales amount
within $1.00 and with 99 percent level of confidence?
11.
A research firm has been asked to estimate the proportion of all
restaurants in the state of Ohio that serve alcoholic beverages. The
firm wants to be 90 percent confident of its results, but has no idea
what the actual proportion is. The firm would like to report an error of
no more than 0.05. How large a sample should it take?
TOPIC 8
HYPOTHESIS TESTING
Terms to Know:
Null hypothesis
Alternative hypothesis
Type I error
Type II error
One-tail test
Two-tail test
Acceptance region
Rejection region
Level of significance
Problems and Interpretation Questions:
1.
The Life Insurance Institute, based on a projection from last year's
figures, claims that the mean face value of the life insurance policies
sold this year is $35,000. A random sample of 49 of this year's policies
has an average face value of $38,000 with a sample standard deviation of
$20,000. Can the Institute's claim be accepted at the .05 level of
significance?
2.
The mean size of the stock purchases by customers of Merrill Lynch last
month was $2,800. This month Merrill Lynch has reduced its sales
commissions hoping to induce larger purchases. A sample of 100 purchases
this month had a mean size of $2,900 with a sample standard deviation of
$1,500. At the .01 significance level, can it be concluded that the
reduced commissions increased average stock purchases?
3.
The manufacturer of a new compact car claims that the car will average at
least 35 miles per gallon in general highway driving. For 40 test runs,
the car averaged 34.5 miles per gallon with a standard deviation of 2.3
miles per gallon. Can the manufacturer's claim be rejected at the 5
percent level of significance?
4.
The average annual income for graduates in their first job after
completing business school was thought to be $28,000. A survey of 144
recent business school graduates found that the average salary was
$28,500 with a standard deviation of $1,200. Test the null hypothesis
that the starting salary of business school graduates is $28,000 at the
1 percent level of significance.
5.
Greyhound claims that at least 90 percent of the packages it delivers
arrive on time. One hundred packages are sent at differing times from
differing locations via Greyhound with the result that eighty packages
arrive on time. Can Greyhound's claim be accepted at the .10
significance level?
6.
The cable comedy channel claims that at least 30 percent of the homes in
Las Vegas watch South Park. An advertiser randomly samples 60 homes and
finds that 15 are watching South Park. Should the comedy channel's claim
be rejected at the 5 percent level of significance?
8.1
8.2
7.
During the 1996 National Football League (NFL) preseason a total of 62
games were played to conclusion. Of this total, 40 games were won by
the home team while the remaining 22 were won by the visiting team.
Test the hypothesis that the population proportion (π) of home team wins
during the NFL preseason is equal to 50 percent using a .05 level of
significance. Interpret the result.
TOPIC 9
SMALL SAMPLE STATISTICS
Terms to Know:
Student's t-distribution
Degrees of freedom
Problems and Interpretation Questions:
1.
An analyst in a personnel department randomly selects the records of 16
hourly employees and finds that the mean wage rate per hour is $9.50.
The wage rates in the firm are assumed to be normally distributed. If
the standard deviation of the wage rates is known to be $1.00, estimate
the mean wage rate in the firm using a 95 percent confidence interval.
2.
A retailer wishes to estimate the mean time it takes for a wholesaler to
fill an order. From a sample of 10 orders, the retailer finds the mean
time is 15 days with a standard deviation of 4 days. Construct a 90
percent confidence interval for the mean time it takes to get an
order filled by the wholesaler.
3.
Burger Chemical of Newark claims that the mean daily amount of pollutants
being emitted from one of its stacks is 880 kilograms. Newark monitors
the stack on 25 randomly selected days in order to see if the mean is
greater or less than 880 kilograms per day. For the 25 sampled days, the
mean was 910 kilograms with a sample standard deviation of 200 kilograms.
At the .05 significance level, can Newark conclude that there has
been a change in the mean amount of pollutants emitted from the stack?
4.
The mean pollution index in Denver was 176 last winter. A random sample
of 12 days this winter yielded a mean of 158 with a standard deviation of
40. At the 1 percent level of significance, can it be concluded that the
pollution index has declined?
9.1
TOPIC 10
REGRESSION ANALYSIS
Terms to Know:
Deterministic model
Stochastic model
Simple regression
Dependent variable
Independent variable
Scatter plot
Least squares criterion
Constant term
Slope coefficient
Standard error of estimate
Residual
Coefficient of determination
Correlation coefficient
Homoscedasticity
Problems and Interpretation Questions:
1.
A railroad is interested in an analysis of how many meals are demanded on
runs of its trains from New York to Florida. Four runs have been sampled
yielding the following data on the number of passengers and the number of
meals demanded:
Passengers (X)
Meals (Y)
____________________________
100
50
150
80
130
70
120
80
____________________________
(a)
Determine the least squares regression equation for this data set.
Explain the equation.
(b)
Calculate the standard error of estimate.
error of estimate measure?
(c)
Test the null hypothesis that the slope of the regression line is
zero using a 10 percent level of significance.
(d)
Calculate the coefficient of determination and the correlation
coefficient. What do the obtained values mean?
10.1
What does the standard
10.2
2.
A large meat packing company
the number of cattle grazing
supermarket price of beef in
been found for the last four
has done a study on the relationship between
and in feed lots as of May and the
the following November. The following has
years:
Cattle (X)
Price (Y)
________________________
800
$1.60
1,000
1.20
1,200
1.10
1,000
1.30
________________________
Solve (a) through (d) given in problem 1.
3.
Explain the assumptions underlying linear regression.
4.
Process the data in problems 1 and 2 above through the Regression
Analysis Tool in the Excel Analysis ToolPak:
(1)
(2)
(3)
Input the data into a spreadsheet and run the regression.
Print the regression output.
Answer questions (a) through (d) using the regression printout.