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MATH399 Statistics—Lab
Week 2
Question 1 is worth 5
points and each question after that is worth 4.5 points, for a total of 50
points for the lab.
Name:_______________________
Statistical Concepts:
·
Using Excel
·
Graphics
·
Shapes of
distributions
·
Descriptive statistics
NOTE: Directions for
all labs are given based on Excel 2013 for Windows. If you have another version
of Excel, you may need to research how to do the same steps.
Data in Excel
Ø Excel is a powerful,
yet user-friendly, data analysis software package. You can launch Excel by
finding the icon and double clicking on it. There are detailed instructions
on how to obtain the graphs and statistics you need for this lab in each
question. There is also a link to an Excel how to document on the iLab page
where you opened this file. Further, if you need more explanation of the Excel
functions you can do an internet search on the function like “Excel standard
deviation” or “Excel pivot table” for a variety of directions and video
demonstrations.
Ø Data have already
been formatted and entered into an Excel worksheet. You will see the link on
the page with this lab document. The names of each variable from the survey are
in the first row of the worksheet. All other rows of the worksheet represent
certain students’ answers to the survey questions. Therefore, the rows are
called observations and the columns are called variables. Below, you will find
a code sheet that identifies the correspondence between the variable names and
the survey questions.
SurveyCode Sheet: Do NOT answer these questions. The code sheet just lists
the variables name and the question used by the researchers on the survey
instrument that produced the data that are included in the Excel data file.
This is just information. The first question for the lab is after the code
sheet.
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Variable Name
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Question
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Drive
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Question 1: How long does it take you to
drive to the school on average (to the nearest minute)?
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State
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Question 2: In what state/country were you
born?
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Shoe
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Question 3: What is your shoe size?
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Height
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Question 4: What is your height to the
nearest inch?
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Sleep
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Question 5: How many hours did you sleep
last night?
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Gender
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Question 6: What is your gender?
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Car
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Question 7: What color of car do you drive?
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TV
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Question 8: How long (on average) do you
spend a day watching TV?
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Money
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Question 9: How much money do you have with
you right now?
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Coin
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Question 10: Flip a coin 10 times. How many
times did you get tails?
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Frequency
Distributions
1. 1. Create a frequency table for the variable State.In the Excel
file, you can click on Data and then Sort and
choose State as the variable on which to sort. Once sorted,
you can count how many students are from each state. From that table, use a
calculator to determine the relative percentages, as well as the cumulative
percentages.
In the box below, type
the states from the database in a column to the left, then type the counts, and
relative and cumulative frequencies to the right of the respective state. Using
the data in the table, make a statement about what the frequency counts or
percentages tell about the data.
Creating Graphs
2.
2. Create a bar chart
for the frequency table in Question 1. Select the State variable values. Click
onInsertand then click on the arrow on the bottom right of the Charts area
and select Clustered Columnand click OK. (Again,
different versions of Excel may need different directions.) Add an appropriate
title and axis label. Copy and paste the graph here.
3. 3. Create a pie chart for the variable Car. Select the column
with the Car variable, including the title of Car. 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.
4. 4. Create a histogram for the variable Height. Use the
strategies in the text to create a frequency table of the heights using the
categories of 60–64, 65–69, 70–74, and 75–79. It may be helpful to sort the
data based on the Height variable first. Create a new worksheet in Excel by
clicking on the + along the bottom of the screen and type in the categories and
the frequency for each category. Then, select the frequency table, click
on Insert, then Recommended Charts and choose the
column chart shown and click OK. Right-click on one of the bars and
select Format Data Series. In the pop up box, change the Gap
Width to 0. Add an appropriate title and axis label.Copy and paste the
graph here.
5.
5. Create a stem and
leaf chart for the variable Money, using only the whole dollar amounts. This
must be done by hand, as Excel cannot do this type of chart. Using the tens
value as the stem and the ones value for the leaves, type a stem and leaf plot
into the box below. It may be helpful to sort the data based on the Money
variable first.
Calculating
Descriptive Statistics
6. 6. 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 Average,thenOK.
Type in the averages below. 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 StdDevthenOK. Type the standard deviations below.
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Mean
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Standard Deviation
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Females
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||
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Males
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Ø Select File > Save
Worksheet As to save the data set. You must either keep a copy of this
data or download it again off the website for future labs.
Short Answer Writing
Assignment
All answers should be
complete sentences.
7. 7. What is the most common color of car for students who
participated in this survey? Explain how you arrived at your answer.
8.
8. What is seen in the
histogram created for the heights of students in this class (include the
shape)? Explain your answer.
9. 9. What is seen in the stem and leaf plot for the money variable
(including the shape)? Explain your answer.
10. 10. 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.
11. 11. 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.
DeVry MATH399 Week 4 iLab
MATH399 Statistics
Week 4 Lab
Name:
_______________________
Statistical Concepts:
·
Probability
·
Binomial Probability
Distribution
Calculating Binomial
Probabilities
Ø Open a new Excel
worksheet.
1. 1. Open spreadsheet
2. 2. In cell A1 type “success” as the label
3. 3. Under that in column A, type 0 through 10 (these will be in
rows 2 through 12)
4. 4. In cell B1, type “one fourth”
5. 5. In cell B2, type “=BINOM.DIST(A2,10,0.25,FALSE)” [NOTE: if
you have Excel 2007, then the formula is BINOMDIST without the period]
6. 6. Then copy and paste this formula in cells B3 through B12
7. 7. In cell C1, type “one half”
8. 8. In cell C2, type “=BINOM.DIST(A2,10,0.5,FALSE)”
9. 9. Copy and paste this formula in cells C3 through C12
10. 10. In cell D1 type “three fourths”
11. 11. In cell D2, type “=BINOM.DIST(A2,10,0.75,FALSE)”
12. 12. Copy and paste this formula in cells D3 through D12
Plotting the Binomial
Probabilities
1. 1. Create plots for the three binomial distributions above. You
can create the scatter plots in Excel by selecting the data you want plotted,
clicking on INSERT, CHARTS, SCATTER, then selecting the first chart shown which
is dots with no connecting lines.Do this two more times and for graph 2 set Y
equal to ‘one half’ and X to ‘success’, and for graph 3 set Y equal to ‘three
fourths’ and X to ‘success’. Paste those three scatter plots in the grey area
below. (12 points)
Calculating
Descriptive Statistics
Ø You will use the
same class survey results that were entered into the Excel worksheet for the
Week 2 iLab Assignment for question 2.
2. 2. Calculate descriptive statistics for the variable(Coin) where
each of the students flipped a coin 10 times. Round your answers to three
decimal places and typethe mean and the standard deviation in the grey area
below. (4 points)
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Mean:
Standard deviation:
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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. 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 sentence
not necessary; round your answers to three decimal places) (10 points)
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P(x=0)
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P(x=6)
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P(x=1)
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P(x=7)
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P(x=2)
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P(x=8)
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P(x=3)
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P(x=9)
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P(x=4)
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P(x=10)
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P(x=5)
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4. 4. Give the probability for the following based on the
calculations in question 3 above, with the probability of a success
being ½. (Complete sentence not necessary; round your answers to three decimal
places) (12 points)
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P(x?1)
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P(x<0)
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|||
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P(x>1)
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P(x?4)
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|||
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P(4<x ?7)
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P(x<4 or x?7)
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5. 5. Calculate (by hand) the mean and standard deviation for the
binomial distribution with the probability of a success being ½and n = 10.
Either show work or explain how your answer was calculated. Use these formulas
to do the hand calculations: Mean = np, Standard Deviation =
.gif”> (4 points)
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Mean = np:
Standard Deviation = .gif”>:
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6. 6. 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. (4 points)
7. 7. Compare the mean and standard deviation for the Coin variable
(question 2) 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. (4 points)
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Mean from question #2:
Standard deviation from question #2:
Mean from question #5:
Standard deviation from question #5:
Comparison and explanation:
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DeVry MATH399 Week 6 iLab
MATH 399N Statistics
for Decision Making
Week 6 iLab
Name:_______________________
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 then find the maximum error. Then we can use a calculator to find the
interval, (x – E, x + E).
First, find the mean.
Under that column, in cell E37, type =AVERAGE(E2:E36). Under that
in cell E38, type =STDEV(E2:E36). Now we can find the maximum error
of the confidence interval. To find the maximum error, we use the “confidence”
formula. In cell E39, type =CONFIDENCE.NORM(0.05,E38,35). The 0.05
is based on the confidence level of 95%, the E38 is the standard deviation, and
35 is the number in our sample. You then need to calculate the confidence
interval by using a calculator to subtract the maximum error from the mean
(x-E) and add it to the mean (x+E).
1. 1. Give and interpret the 95% confidence interval for the hours
of sleep a student gets. (5 points)
Then, you can go down
to cell E40 and type =CONFIDENCE.NORM(0.01,E38,35) to find the
maximum error for a 99% confidence interval. Again, you would need to use a
calculator to subtract this and add this to the mean to find the actual
confidence interval.
2. 2. Give and interpret the 99% confidence interval for the hours
of sleep a student gets. (5 points)
3. 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. (10 points)
4. 4. Find the mean and standard deviation of the DRIVE variable by
using =AVERAGE(A2:A36) and =STDEV(A2:A36).
Assuming that this variable is normally distributed, what percentage of data
would you predict would be less than 40 miles? This would be based on the
calculated probability. Use the formula =NORM.DIST(40, mean,
stdev,TRUE). Now determine the percentage of data points in the dataset
that fall within this range. 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? (15 points)
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Mean ______________ Standard deviation
____________________
Predicted percentage
______________________________
Actual percentage
_____________________________
Comparison
___________________________________________________
______________________________________________________________
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5. 5. 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?
Subtract the probabilities found through =NORM.DIST(70, mean, stdev,
TRUE) and =NORM.DIST(40, mean, stdev, TRUE) for the
“between” probability. To get the probability of over 70, use the same =NORM.DIST(70,
mean, stdev, TRUE) and then subtract the result from 1 to get “more
than”. 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? (15 points)
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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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