If you were
given a large data set, such as the sales over the last year of our top 100
customers, what might you be able to do with these data? What might be the benefits
of describing the data?
Alternative:
Look for examples of descriptive statistics in the news or on websites. Then post a link to that publication or site,
note the statistic used and determine if it was an appropriate use of that
statistic.
Look online
and find an article published within the past 4 weeks that includes a reference
to probabilities, means, or standard deviations. These articles might be discussing weather events,
investing outcomes, or sports performance, among many other possible topics.
Your first
post should include a summary of the article and what numbers you are
highlighting from that article. Also
include a link to the actual article. In
your replies to other students, describe specific decisions that the statistic
might influence and whether a different statistic might be more appropriate.
For this
discussion you will use technology to create a short 1-2 minute multimedia
post/presentation.
Suggestions:
Narrated PowerPoint, recorded video (.mp4), Screencast-O-Matic (.mp4), or a
similar tool of your choice. Video can be recorded directly within a post as
well, but make sure to plan out in advance what you are going to say/show.
There should be a visual component as well as audio, so if you are using a
webcam for the video that only shows you speaking, please attach your
PowerPoint slide(s) (or screenshot images of them) to the post as well so
everyone can see them.
In your
short presentation, you will be describing an example that uses discrete
probabilities or distributions. Provide an example that follows either the
binomial probabilities or any discrete probability distribution, and explain
why that example follows that distribution. In your responses to other
students, make up numbers for the example provided by that other student, and
ask a related probability question. Then show the work (or describe the technology
steps) and solve that probability example.
For more
information about Narrated PowerPoint, access the Student Resources section of
Course Resources under the Introduction & Resources module heading, and
look for the heading that corresponds to the tool you want to use. For all
media posts in this course, please include a brief written synopsis to inform
your classmates what the main point or purpose is that the linked, attached, or
embedded media addresses.
Assume that
a population is normally distributed with a mean of 100 and a standard
deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or
more? Why or why not?
Look in the
newspapers, magazines, and other news sources for results of a survey or poll
that show the confidence interval, usually shows as a +/- some amount. Describe the survey or poll and then describe
the interval shown. How does knowing the
interval, rather than just the main result, impact your view of the results?
Consider a
business of any type. What is a
situation where a hypothesis test might help make a decision? Describe the situation. Then you or someone in a reply can make up
numbers for that situation and someone else can solve it.
Suppose you
are given data from a survey showing the IQ of each person interviewed and the
IQ of his or her mother. That is all the information that you have. Your boss
has asked you to put together a report showing the relationship between these
two variables. What could you present and why?
MATH221 Statistics for Decision MakingWeek 8 REFLECTION PAPER
The
Reflection Paper is due this week. Please refer to the Reflection Paper
Overview for a full description of this assignment
Please
remember to submit your assignment BEFORE the due date.
Note: This
assignment uses TurnItIn. To review the TurnItIn results for your submitted
paper, look for this assignment in the Gradebook and click the colored icon to
open the TurnItIn Originality Report.
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
MATH221 Statistics for Decision Making
Week 3 Quiz
Question 1
(CO 1) Among 500 people at the concert, a survey of 35 found 28% found it too
loud. What is the population and what is the sample?
Population: 500 at that concert; Sample: the
35 in the survey
Population: all concert goers; Sample: the
28% who found it too loud
Population: 500 at that concert: Sample: the
28% who found it too loud
Population: all concert goers; Sample: the
500 at that concert
Question
2(CO 1) A survey of 481 of your customers shows that 79% of them like the
recent changes to the product. Is this percentage a parameter or a statistic
and why?
Parameter as it represents the sample
Statistic as it represents the population
Parameter as it represents the population
Statistic as it represents the sample
Question
3(CO 1) Classify the data of the top grossing movies for 2017.
Statistics
Qualitative
Quantitative
Classical
Question
4(CO 1) The data set that lists the number of performances for each Broadway
show in 2017 would be classified as what type of data?
Ratio
Nominal
Interval
Ordinal
Question
5(CO 1) A data set that includes the number of products that were produced
within each hour by a company would be classified as what type of data?
Ordinal
Ratio
Nominal
Interval
Question
6(CO 1) What type of data collection might be best to estimate the impact of
exercise on longevity?
Simulation
Experiment
Survey
Observational
Question
7(CO 1) What type of data collection might be best to study how voters might
decide an upcoming ballot issue?
Simulation
Survey
Observational
Experiment
Question
8CO 1) You need to study the satisfaction of customers of a specific
restaurant. You decide to randomly select one customer at each table. This
would most closely describe which type of sampling technique?
Stratified
Random
Cluster
Systematic
Question
9(CO 1) Which of the following graphs would be a Pareto chart?
Vertical bars with spaces between with
highest to left and shortest to right
Horizontal bars with various lengths
Vertical base with spaces between of various
heights
Vertical bars with various lengths
Question
10(CO 1) In a normally distributed data set of how long customers stay in your
store, the mean is 31.7 minutes and the standard deviation is 1.9minutes .
Within what range would you expect 95% of your customers to stay in your store?
27.9-35.5
30.75-32.7
29.8-33.6
26.0-37.4
MATH221 Statistics for Decision Making
Week 5 Quiz
Question
1(CO 3) Consider the following table:
Age Group Frequency
18-29 983
30-39 784
40-49 686
50-59 632
60-69 541
70 and over 527
If you
created the probability distribution for these data, what would be the
probability of 30-39?
0.165
0.237
0.425
0.189
Question 2(CO 3) Consider the following table
of hours worked by part-time employees. These employees must work in 5 hour
blocks.
Weekly
hours worked Probability
5 0.06
15 0.61
20 0.18
25 0.15
Find the
mean of this variable.
12.20
17.50
18.95
16.80
Question 3(CO 3) Consider the following table.
Defects in
batch Probability
0 0.30
1 0.28
2 0.21
3 0.09
4 0.08
5 0.04
Find the
variance of this variable.
1.49
0.67
1.41
1.99
Question 4(CO 3) Consider the following table:
Defects in
batch Probability
0 0.21
1 0.28
2 0.30
3 0.09
4 0.08
5 0.04
Find the
standard deviation of this variable.
1.33
1.67
1.78
1.41
Question 5(CO 3) Twenty-two percent of US
teens have heard of a fax machine. You randomly select 12 US teens. Find the
probability that the number of these selected teens that have heard of a fax
machine is exactly six (first answer listed below). Find the probability that
the number is more than 8 (second answer listed below).
0.024, 0.001
0.993, 0.000
0.993, 0.024
0.024, 0.000
Question 6(CO 3) Ten rugby balls are randomly selected
from the production line to see if their shape is correct. Over time, the
company has found that 85.2% of all their rugby balls have the correct shape.
If exactly 7 of the 10 have the right shape, should the company stop the
production line?
Yes, as the probability of seven having the
correct shape is not unusual
Yes, as the probability of seven having the
correct shape is unusual
No, as the probability of seven having the
correct shape is not unusual
No, as the probability of seven having the
correct shape is unusual
Question 7(CO 3) A bottle of water is supposed
to have 12 ounces. The bottling company has determined that 98% of bottles have
the correct amount. Which of the following describes a binomial experiment that
would determine the probability that a case of 36 bottles has all bottles
properly filled?
n=12, p=36, x=98
n=36, p=0.98, x=36
n=36, p=0.98, x=12
n=0, p=0.98, x=36
Question 8(CO 3) On the production line the
company finds that 95.6% of products are made correctly. You are responsible
for quality control and take batches of 30 products from the line and test
them. What number of the 30 being incorrectly made would cause you to shut down
production?
Less than 26
Less than 28
Less than 27
More than 25
Question 9(CO 3) The probability of someone
ordering the daily special is 52%. If the restaurant expected 65 people for
lunch, how many would you expect to order the daily special?
34
35
30
31
Question 10(CO 3) Fifty-seven percent of
employees make judgements about their co-workers based on the cleanliness of
their desk. You randomly select 8 employees and ask them if they judge
co-workers based on this criterion. The random variable is the number of
employees who judge their co-workers by cleanliness. Which outcomes of this
binomial distribution would be considered unusual?
0, 1, 8
1, 2, 8
1, 2, 8
0, 1, 2, 8
MATH221 Statistics for Decision Making
Week 7 Quiz
Question 1(CO
4) From a random sample of 55 businesses, it is found that the mean time that
employees spend on personal issues each week is 4.9 hours with a standard
deviation of 0.35 hours. What is the 95% confidence interval for the amount of
time spent on personal issues?
(4.81, 4.99)
(4.84, 4.96)
(4.83, 4.97)
(4.82, 4.98)
Question 2(CO
4)If a confidence interval is given from 8.50 to 10.25 and the mean is known to
be 9.375, what is the margin of error?
1.750
0.875
8.500
0.438
Question 3(CO
4) If the population standard deviation of a increases without other changes,
what is most likely to happen to the confidence interval?
does not change
widens
cannot determine
narrows
Question 4(CO
4) From a random sample of 41 teens, it is found that on average they spend
43.1 hours each week online with a population standard deviation of 5.91 hours.
What is the 90% confidence interval for the amount of time they spend online
each week?
(37.19, 49.01)
(40.58, 45.62)
(31.28, 54.92)
(41.58, 44.62)
Question 5(CO
4) A company making refrigerators strives for the internal temperature to have
a mean of 37.5 degrees with a population standard deviation of 0.6 degrees,
based on samples of 100. A sample of 100 refrigerators have an average
temperature of 37.48 degrees. Are the refrigerators within the 90% confidence
interval?
Yes, the temperature is within the confidence
interval of (37.40, 37.60)
Yes, the temperature is within the confidence
interval of (36.90, 38.10)
No, the temperature is outside the confidence
interval of (36.90, 38.10)
No, the temperature is outside the confidence
interval of (37.40, 37.60)
Question 6(CO
4) What is the 97% confidence interval for a sample of 104 soda cans that have
a mean amount of 15.10 ounces and a population standard deviation of 0.08
ounces?
(15.940, 15.260)
(15.083, 15.117)
(12.033, 12.067)
(15.020, 15.180)
Question 7(CO
4) Determine the minimum sample size required when you want to be 98% confident
that the sample mean is within two units of the population mean. Assume a
population standard deviation of 5.75 in a normally distributed population.
45
23
43
44
Question 8(CO
4) Determine the minimum sample size required when you want to be 80% confident
that the sample mean is within 1.5 units of the population mean. Assume a
population standard deviation of 9.24 in a normally distributed population.
62
146
145
63
Question 9(CO
4) Determine the minimum sample size required when you want to be 75% confident
that the sample mean is within thirty units of the population mean. Assume a
population standard deviation of 327.8 in a normally distributed population
158
324
197
157
Question 10(CO
4) In a sample of 8 high school students, they spent an average of 28.8 hours
each week doing sports with a sample standard deviation of 3.2 hours. Find the
95% confidence interval, assuming the times are normally distributed.
(25.62, 32.48)
(24.10, 34.50)
(26.12, 31.48)
(22.47, 35.21)
MATH221 Statistics for Decision Making
Week 2 LAB
Creating
Graphs
1. Create a pie chart for the variable
Car Color: Select the column with the Car variable, including the title of Car
Color. Click on Insert, and then
Recommended Charts. It should show a
clustered column and click OK. Once the
chart is shown, right click on the chart (main area) and select Change Chart Type. Select Pie and OK. Click on the pie slices, right click Add Data
Labels, and select Add Data Callouts.
Add an appropriate title. Copy
and paste the chart here.
2. Create a histogram for the variable
Height. You need to create a frequency distribution for the data by hand. Use 5 classes, find the class width, and then
create the classes. Once you have the
classes, count how many data points fall within each class. It may be helpful
to sort the data based on the Height variable first. Once you have the classes and the frequency
counts, put those data into the table in the Freq Distribution worksheet of the
Week 1 Excel file. Copy and paste the
graph here.
3. Create
a scatter plot with the variables of height and money. Copy the height variable from the data file
and paste it into the x column in the Scatter Plot worksheet of the week 1
Excel file. Copy the money variable from
the data file and paste it into the y column.
Copy and paste the scatter plot below.
Calculating
Descriptive Statistics
4. Calculate descriptive statistics for
the variable Height by Gender. Sort the
data by gender by clicking on Data and then Sort. Copy the heights of the males form the data
file into the Descriptive Statistics worksheet of the week 1 Excel file. Type the standard deviations below. These are
sample data. Then from the data file, copy and paste the female data into the
Descriptive Statistics workbook and do the same
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Mean
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Standard deviation
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Females
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Males
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All answers
should be complete sentences.
5. What is the most common color of car
for students who participated in this survey? Explain how you arrived at your
answer.
6. What is seen in the histogram
created for the heights of students in this class (include the shape)? Explain
your answer.
7. What is seen in the scatter plot for
the height and money variables? Explain your answer.
8. Compare the mean for the heights of
males and the mean for the heights of females in these data. Compare the values
and explain what can be concluded based on the numbers.
9. Compare the standard deviation for
the heights of males and the standard deviation for the heights of females in
the class. Compare the values and explain what can be concluded based on the
numbers.
10. Using the empirical rule, 95% of
female heights should be between what two values? Either show work or explain
how your answer was calculated.
11. Using the empirical rule, 68% of male
heights should be between what two values? Either show work or explain how your
answer was calculated.
MATH221 Statistics for Decision Making
Week 4 LAB
Calculating
Binomial Probabilities
NOTE: For question 1, you will be using the same
data file your instructor gave you for the Week 2 Lab.
1.Using the
data file from your instructor (same one you used for the Week 2 Lab),
calculate descriptive statistics for the variable (Coin) where each of the
thirty-five students in the sample flipped a coin 10 times. Round your answers
to three decimal places and type the mean and the standard deviation in the
grey area below.
Plotting
the Binomial Probabilities
? For the next part of the lab, open
the Week 3 Excel worksheet. This will be
used for the next few questions, rather than the data file used for the first
question.
1. Click on the “binomial tables”
workbook
2.Type in
n=10 and p=0.5; this simulates ten flips of a coin where x is counting the
number of heads that occur throughout the ten flips
3.Create a
scatter plot, either directly in this spreadsheet (if you are comfortable with
those steps), or by using the Week 1 spreadsheet and copying the data from here
onto that sheet (x would be the x variable, and P(X=x) would be the y variable.
4. Repeat steps 2 and 3 with n=10 and
p=0.25
5. Repeat steps 2 and 3 with n=10 and
p=0.75
6. In the end, you will have three
scatter plots for the first question below.
2. Create scatter plots for the
binomial distribution when p=0.50, p=0.25, and p=0.75 (see directions
above). Paste the three scatter plots in
the grey area below.
Calculating
Descriptive Statistics
Short
Answer Writing Assignment – Both the calculated binomial probabilities and the
descriptive statistics from the class database will be used to answer the
following questions. Round all numeric answers
to three decimal places.
3.List the
probability value for each possibility in the binomial experiment calculated at
the beginning of this lab, which was calculated with the probability of a
success being ½. (Complete sentences not necessary; round your answers to three
decimal places.)
P(x=0) P(x=6)
P(x=1) P(x=7)
P(x=2) P(x=8)
P(x=3) P(x=9)
P(x=4) P(x=10)
P(x=5)
4.Give the
probability for the following based on the calculations in question 3 above,
with the probability of a success being ½. (Complete sentences not necessary;
round your answers to three decimal places.)
5.Calculate
(by hand) the mean and standard deviation for the binomial distribution with
the probability of a success being ½ and n = 10. Either show your work or
explain how your answer was calculated. Use these formulas to do the hand
calculations: Mean = np, Standard Deviation =
6.Calculate
(by hand) the mean and standard deviation for the binomial distribution with
the probability of a success being ¼ and n = 10. Write a comparison of these
statistics to those from question 5 in a short paragraph of several complete
sentences. Use these formulas to do the hand calculations: Mean = np, Standard
Deviation =
7.Calculate
(by hand) the mean and standard deviation for the binomial distribution with
the probability of a success being ¾ and n = 10. Write a comparison of these
statistics to those from question 6 in a short paragraph of several complete
sentences. Use these formulas to do the hand calculations: Mean = np, Standard
Deviation =
8.Using all
four of the properties of a Binomial experiment (see page 201 in the textbook)
explain in a short paragraph of several complete sentences why the Coin
variable from the class survey represents a binomial distribution from a
binomial experiment.
9.Compare
the mean and standard deviation for the Coin variable (question 1) with those
of the mean and standard deviation for the binomial distribution that was
calculated by hand in question 5. Explain how they are related in a short
paragraph of several complete sentences.
MATH221 Statistics for Decision Making
Week 6 LAB
Scenario/Summary
Click to
download the Week 6 Lab Document (Links to an external site.) to complete the
lab for this week. All of the directions
are included in the document.
The data
for this lab is distributed by your professor.
The
document includes places where you need to input the answers. Any place where
you see a gray box is where you need to put an answer.
Deliverables
Each
student will submit a lab. Below is the
grading rubric for this assignment.
Category Points % Description
Questions
1-5 8 points each, 40 total 50% large
and small sample confidence intervals for a mean
Question 6 16 points 20% normal
probabilities compared with data outcomes
Question 7 24 points 30% normal
probabilities compared with data outcomes
Total 80 points 100% A quality lab will meet or exceed all of
the above requirements.
Required
Software
Microsoft
Office: Word and Excel
Use a
personal copy or access the software at https://lab.devry.edu (Links to an
external site.).
Lab Steps
Prepare and
Submit Lab
Open Excel.
Open the
lab Word document.
Follow the
steps in the lab Word document to do calculations in Excel.
Copy and
paste from Excel into the Word document or retype the answer, and then complete
the answers to the questions in complete sentences (fill in each gray box in
the Word document).
Save the
lab Word document, and submit it; no other files should be submitted
Statistical Concepts:
·
Data Simulation
·
Confidence Intervals
·
Normal Probabilities
Short Answer Writing Assignment
All answers should be complete
sentences.
We need to find the confidence interval for the SLEEP
variable. To do this, we need to find
the mean and standard deviation with the Week 1 spreadsheet. Then we can the Week 5 spreadsheet to find
the confidence interval.
First, find the mean and standard deviation by copying the
SLEEP variable and pasting it into the Week 1 spreadsheet. Write down the mean and the sample standard
deviation as well as the count. Open the Week 5 spreadsheet and type in the
values needed in the green cells at the top. The confidence interval is shown
in the yellow cells as the lower limit and the upper limit.
1. Give and interpret the 95%
confidence interval for the hours of sleep a student gets.
Change the confidence level to 99% to find the 99% confidence
interval for the SLEEP variable.
2. Give and interpret the 99%
confidence interval for the hours of sleep a student gets.
3. Compare the 95% and 99%
confidence intervals for the hours of sleep a student gets. Explain the
difference between these intervals and why this difference occurs.
In the Week 2 Lab, you found the mean and the standard
deviation for the HEIGHT variable for both males and females. Use those values for follow these directions
to calculate the numbers again.
(From Week 2 Lab: Calculate descriptive statistics for the
variable Height by Gender. Click on Insert and then Pivot Table. Click in the
top box and select all the data (including labels) from Height through Gender. Also click on “new worksheet” and then OK.
On the right of the new sheet, click on Height and Gender,
making sure that Gender is in the Rows box and Height is in the Values
box. Click on the down arrow next to Height in the Values box and select Value
Field Settings. In the pop up box,
click Averagethen OK.
Write these down. Then click on
the down arrow next to Height in the
Values box again and select Value Field Settings. In the pop up box, click on StdDevthen OK. Write these values
down.)
You will also need the number of males and the number of females
in the dataset. You can either use the
same pivot table created above by selecting Count in the Value Field
Settings, or you can actually count in the dataset.
Then use the Week 5 spreadsheet to calculate the following
confidence intervals. The male
confidence interval would be one calculation in the spreadsheet and the females
would be a second calculation.
4.
Give and
interpret the 95% confidence intervals for males and females on the HEIGHT
variable. Which is wider and why?
5.
Give and
interpret the 99% confidence intervals for males and females on the HEIGHT
variable. Which is wider and why?
6.
Find the mean and standard deviation of the DRIVE
variable by copying that variable into the Week 1 spreadsheet. Use the Week 4 spreadsheet to determine the
percentage of data points from that data set that we would expect to be less
than 40. To find the actual percentage
in the dataset, sort the DRIVE variable and count how many of the data points
are less than 40 out of the total 35 data points. That is the actual percentage. How does this compare with your
prediction?
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Mean ______________ Standard deviation
____________________
Predicted percentage
______________________________
Actual percentage _____________________________
Comparison
___________________________________________________
______________________________________________________________
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7.
What percentage of data would you predict would be
between 40 and 70 and what percentage would you predict would be more than 70
miles? Use the Week 4 spreadsheet again
to find the percentage of the data set we expect to have values between 40 and
70 as well as for more than 70. Now
determine the percentage of data points in the dataset that fall within this
range, using same strategy as above for counting data points in the data
set. How do each of these compare with
your prediction and why is there a difference?
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Predicted percentage between 40
and 70 ______________________________
Actual percentage
_____________________________________________
Predicted percentage more than 70
miles ________________________________
Actual percentage
___________________________________________
Comparison
____________________________________________________
_______________________________________________________________
Why?
__________________________________________________________
________________________________________________________________
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