MATH221 Statistics for Decision Making
Week 1 Homework
Question 1 The age of every fourth person entering a
department store. The selected individuals would be considered a:
Homework
Help:
1DA.
Population/parameter/sample/statistic/inferential/descriptive (Links to an
external site.) (DOCX)
Parameter
Sample
Population
Statistic
Question 2 In
a survey of 1000 adults, 34% found they prefer charcoal to gas grills. The 1000
would be considered a:
Homework
Help:
1DA.
Population/parameter/sample/statistic/inferential/descriptive (Links to an
external site.) (DOCX)
Population
Sample
Statistic
Parameter
Question 3 The
chances of winning the Maryland lottery are one chance in twenty-two million.
The probability would be considered an example of:
Homework
Help:
1DA.
Population/parameter/sample/statistic/inferential/descriptive (Links to an
external site.) (DOCX)
Experiment design
A sample
Inferential statistics
Descriptive statistics
Question 4 The
ages of 20 first graders would be considered:
Homework
Help:
1DB.
Qualitative/quantitative/nominal/ordinal/interval/ratio (Links to an external
site.) (DOCX)
Qualitative data
Interval data
Nominal data
Quantitative data
Question 5
Marriage
status (married, single, etc.) of the faculty at a university would be
considered:
Homework
Help:
1DB.
Qualitative/quantitative/nominal/ordinal/interval/ratio (Links to an external
site.) (DOCX)
Qualitative data
Ordinal data
Quantitative data
Ratio data
MATH221 Statistics for Decision Making
Week 2 Homework
Question 1 According
to company records, the probability that a washing machine will break in the
first year is 4%. This would be considered:
Homework
Help:
2DA.
Definition of probabilities and classical, empirical, subjective probabilities
(Links to an external site.) (DOCX)
Classical probability
Subjective probability
Manufactured probability
Empirical probability
Question 2 Given
the following information, find the probability that a randomly selected
student will be very short. Number of students who are very short: 45, short:
60, tall: 82, very tall: 21
Homework
Help:
2DB.
Probabilities from a given distribution of frequencies (Links to an external
site.) (DOCX)
21.0%
28.8%
21.6%
39.4%
Question 3 Given the following information,
find the probability that a randomly selected dog will be a golden retriever or
a poodle. Number of dogs who are poodles: 31, golden retrievers: 58, beagles:
20, pugs: 38
Homework
Help:
2DB.
Probabilities from a given distribution of frequencies (Links to an external
site.) (DOCX)
60.5%
46.9%
39.5%
58.0%
Question 4 Given
that there is a 22% chance it will rain on any day, what is the probability
that it will rain on the first day and be clear (not rain) on the next two
days?
Homework
Help:
2VA:
Probabilities given probability of success and 2 or more events (Links to an
external site.) (0:51)
2DC.
Probabilities given probability of success and 2 or more events (Links to an
external site.) (DOCX)
13.4%
17.2%
1.1%
78.0%
Question 5 Consider
the following table. What is the probability of red?
Red Blue Total
Yes 15 21 36
No 38 13 51
Total 53 34 87
Homework
Help:
2VB:
Conditional probabilities from a table (Links to an external site.) (1:45)
15/53
36/87
15/87
53/87
MATH221 Statistics for Decision Making
Week 3 Homework
Question
1Let x represent the number of pets in pet stores. This would be considered
what type of variable:
Homework
Help:
3DA.
Discrete versus continuous variables (Links to an external site.) (DOCX)
Discrete
Nonsensical
Lagging
Continuous
Question 2Let x represent the height of corn
in Oklahoma. This would be considered what type of variable:
Homework
Help:
3DA.
Discrete versus continuous variables (Links to an external site.) (DOCX)
Distributed
Discrete
Continuous
Inferential
Question 3Consider the following table.
Age Group Frequency
18-29 9831
30-39 7845
40-49 6869
50-59 6323
60-69 5410
70 and over 5279
If you
created the probability distribution for these data, what would be the
probability of 40-49?
Homework
Help:
3DB.
Probabilities from a probability distribution (Links to an external site.)
(DOCX)
42.5%
23.7%
18.9%
16.5%
Question 4Consider the following table.
Weekly
hours worked Probability
1-30
(average=23) 0.08
31-40
(average=36) 0.16
41-50
(average=43) 0.72
51 and over
(average=54) 0.04
Find the mean of this variable.
Homework
Help:
3VA.
Calculating the mean, variance, and standard deviation of discrete variables
(Links to an external site.) (4:35)
3DC. Mean,
expected value, variance, and standard deviation of discrete variables (Links
to an external site.) (DOCX)
39.0
40.7
39.5
40.0
Question
5Consider the following table.
Defects in
batch Probability
0 0.09
1 0.24
2 0.41
3 0.12
4 0.10
5 0.04
Find the variance of this variable.
Homework
Help:
3VA.
Calculating the mean, variance, and standard deviation of discrete variables
(Links to an external site.) (4:35)
3DC. Mean,
expected value, variance, and standard deviation of discrete variables (Links
to an external site.) (DOCX)
1.48
1.43
1.22
2.02
MATH221 Statistics for Decision Making
Week 4 Homework
Question 1 The
length of time a person takes to decide which shoes to purchase is normally
distributed with a mean of 8.54 minutes and a standard deviation of 1.91. Find
the probability that a randomly selected individual will take less than 5
minutes to select a shoe purchase. Is this outcome unusual?
Homework
Help:
4VA.
Calculating normal probabilities (Links to an external site.) (2:18)
4DA.
Description of normal distribution, area, and probabilities, definition of unusual
events (Links to an external site.) (DOCX)
Probability is 0.03, which is usual as it is
not less than 5%
Probability is 0.97, which is unusual as it
is greater than 5%
Probability is 0.03, which is unusual as it
is less than 5%
Probability is 0.97, which is usual as it is
greater than 5%
Question 2 Monthly
water bills for a city have a mean of $108.43 and a standard deviation of
$36.98. Find the probability that a randomly selected bill will have an amount
greater than $173, which the city believes might indicate that someone is
wasting water. Would a bill that size be considered unusual?
Homework
Help:
4VA.
Calculating normal probabilities (Links to an external site.) (2:18)
4DA.
Description of normal distribution, area, and probabilities, definition of
unusual events (Links to an external site.)(DOCX)
Probability is 0.04, which is unusual as it
is not less than 5%
Probability is 0.04, which is usual as it is
less than 5%
Probability is 0.04, which is unusual as it
is less than 5%
Probability is 0.04, which is usual as it is
not less than 5%
Question 3 In
a health club, research shows that on average, patrons spend an average of 42.5
minutes on the treadmill, with a standard deviation of 4.8 minutes. It is
assumed that this is a normally distributed variable. Find the probability that
randomly selected individual would spent between 30 and 40 minutes on the
treadmill.
Homework
Help:
4VA.
Calculating normal probabilities (Links to an external site.) (2:18)
4DA.
Description of normal distribution, area, and probabilities, definition of
unusual events (Links to an external site.)(DOCX)
0.70
Less than 1%
0.40
0.30
Question 4 A
tire company measures the tread on newly-produced tires and finds that they are
normally distributed with a mean depth of 0.98mm and a standard deviation of
0.35mm. Find the probability that a randomly selected tire will have a depth
less than 0.50mm. Would this outcome warrant a refund (meaning that it would be
unusual)?
Homework
Help:
4VA.
Calculating normal probabilities (Links to an external site.) (2:18)
4DA.
Description of normal distribution, area, and probabilities, definition of
unusual events (Links to an external site.)(DOCX)
Probability of 0.09 and would not warrant a
refund
Probability of 0.09 and would warrant a
refund
Probability of 0.91 and would warrant a
refund
Probability of 0.91 and would not warrant a
refund
Question 5 A
grocery stores studies how long it takes customers to get through the speed
check lane. They assume that if it takes more than 10 minutes, the customer
will be upset. Find the probability that a randomly selected customer takes
more than 10 minutes if the average is 7.45 minutes with a standard deviation
of 1.04 minutes.
Homework
Help:
4VA.
Calculating normal probabilities (Links to an external site.) (2:18)
4DA.
Description of normal distribution, area, and probabilities, definition of
unusual events (Links to an external site.)(DOCX)
0.007
0.501
0.993
0.071
MATH221 Statistics for Decision Making
Week 5 Homework
Question 1 From
a random sample of 58 businesses, it is found that the mean time the owner
spends on administrative issues each week is 21.69 with a population standard
deviation of 3.23. What is the 95% confidence interval for the amount of time spent
on administrative issues?
Homework
Help:
5VA.
Calculating confidence intervals (Links to an external site.) (4:04)
5DA.
Concept and meaning of confidence intervals (Links to an external site.) (DOCX)
(21.78, 22.60)
(19.24, 24.14)
(20.71, 22.67)
(20.86, 22.52)
Question 2 If
a confidence interval is given from 43.83 up to 61.97 and the mean is known to
be 52.90, what is the margin of error?
Homework
Help:
5DB.
Finding margin of error from given confidence interval (Links to an external
site.) (DOCX)
43.83
18.14
4.54
9.07
Question 3 If
a car manufacturer wanted lug nuts that fit nearly all the time, what characteristics
would be better?
Homework
Help:
5DC.
Confidence intervals in manufacturing, high vs low level of confidence, wide vs
narrow (Links to an external site.) (DOCX)
narrow confidence interval at low confidence
level
wide confidence interval with high confidence
level
wide confidence interval with low confidence
level
narrow confidence interval at high confidence
level
Question 4 Which
of the following are most likely to lead to a narrow confidence interval?
Homework
Help:
5DD.
Changes in confidence interval based on changes in standard deviation or sample
size (Links to an external site.) (DOCX)
large standard deviation
large mean
small sample size
small standard deviation
Question 5 If
you were designing a study that would benefit from very disperse data points,
you would want the input variable to have:
Homework
Help:
5DC.
Confidence intervals in manufacturing, high vs low level of confidence, wide vs
narrow (Links to an external site.) (DOCX)
5DD.
Changes in confidence interval based on changes in standard deviation or sample
size (Links to an external site.) (DOCX)
a small margin of error
a large standard deviation
a large sample size
a large mean
MATH221 Statistics for Decision Making
Week 6 Homework
Question 1A
consumer analyst reports that the mean life of a certain type of alkaline
battery is more than 63 months. Write the null and alternative hypotheses and
note which is the claim.
Homework
Help:
6DA. Theory
and basics of writing hypotheses (Links to an external site.) (DOCX)
Ho: ? ? 63, Ha: ? < 63 (claim)
Ho: ? = 63 (claim), Ha: ? ? 63
Ho: ? ? 63, Ha: ? > 63 (claim)
Ho: ? > 63 (claim), Ha: ? ? 63
Question 2A
business claims that the mean time that customers wait for service is at most
5.9 minutes. Write the null and alternative hypotheses and note which is the
claim.
Homework
Help:
6DA. Theory
and basics of writing hypotheses (Links to an external site.) (DOCX)
Ho: ? > 5.9 (claim), Ha: ? > 5.9
Ho: ? ? 5.9, Ha: ? ? 5.9 (claim)
Ho: ? ? 5.9 (claim), Ha: ? > 5.9
Ho: ? > 5.9, Ha: ? ? 5.9 (claim)
Question
3An amusement park claims that the average daily attendance is at least 20,000.
Write the null and alternative hypotheses and note which is the claim.
Homework
Help:
6DA. Theory
and basics of writing hypotheses (Links to an external site.) (DOCX)
Ho: ? > 20000 (claim), Ha: ? = 20000
Ho: ? ? 20000, Ha: ? > 20000 (claim)
Ho: ? ? 20000 (claim), Ha: ? < 20000
Ho: ? = 20000, Ha: ? ? 20000 (claim)
Question 4A transportation organization claims
that the mean travel time between two destinations is about 23 minutes. Write
the null and alternative hypotheses and note which is the claim.
Homework
Help:
6DA. Theory
and basics of writing hypotheses (Links to an external site.) (DOCX)
Ho: ? > 23, Ha: ? ? 23 (claim)
Ho: ? ? 23, Ha: ? = 23 (claim)
Ho: ? = 23 (claim), Ha: ? ? 23
Ho: ? = 23 (claim), Ha: ? ? 23
Question 5If
the null hypothesis is not rejected when it is false, this is called
__________.
Homework
Help:
6DB. Type I
and type II errors (Links to an external site.) (DOCX)
the Empirical Rule
an alternative hypothesis
a type I error
a type II error
MATH221 Statistics for Decision Making
Week 7 Homework
Question
1Two variables have a negative non-linear correlation. Does the dependent
variable increase or decrease as the independent variable increases?
Homework
Help:
7DA.
Linear, non-linear, positive and negative correlations (Links to an external
site.) (PDF)
Dependent variable decreases
Dependent variable increases
Cannot determine from information given
Dependent variable would remain the same
Question 2What does the variable r represent?
Homework
Help:
7DB.
Correlation coefficient and coefficient of determination, notation and meanings
(Links to an external site.) (PDF)
The coefficient of determination
The sample correlation coefficient
The population correlation coefficient
The critical value for the correlation
coefficient
Question 3A golfer wants to determine if the
type of driver she uses each year can be used to predict the amount of
improvement in her game. Which variable would be the explanatory variable?
Homework
Help:
7DA.
Linear, non-linear, positive and negative correlations (Links to an external
site.) (PDF)
7DC.
Explanatory and response variables (Links to an external site.) (PDF)
The number of holes she plays
The improvement in her game
The type of driver
The rating of the golfer
Question 4Two variables have a positive linear
correlation. Where would the y-intercept of the regression line be located on
the y-axis?
Homework
Help:
7DA.
Linear, non-linear, positive and negative correlations (Links to an external
site.) (PDF)
Below 0
To the left of 0
Cannot determine
To the right of 0
Question 5A value of the dependent variable
that corresponds to the value of xi would be given the notation of:
Homework
Help:
7DD.
Regression notation of m, b, y1, x1, yi, xi, means of variables, estimates of
variables (Links to an external site.) (PDF)
y1
b
m
yi