Download Handout - CMC3

CMC3-South Conference - Anaheim
March 14, 2015
A Visual path from Z to t to ANOVA
By: Tuyetdong Phan-Yamada – Glendale Community College
Website: https://sites.google.com/site/phanyamada/Home/teaching/statistics
Email: [email protected]
GeoGebra Commands and Tests for Statistics
Download free GeoGebra at http://www.geogebra.org/cms/en/download/
All statistics files can be found at
https://sites.google.com/site/phanyamada/Home/teaching/statistics
1. Calculate the probability of a binomial distribution: Open a new ggb file. On the spreadsheet
screen, click on the histogram symbol button. From the drop down menu, select Probability
Calculator. On the Distribution box, choose Binomial. Enter value for n and p. On the Probability
box, select your option and limits.
2. Calculate the mean and standard deviation of probability distribution: Open the Probability
Distribution.ggb. Type the Observed and Expected frequencies on the Spreadsheet screen. Enter the
number of data n on the Graphic Screen.
3. Random Integers: Randomly pick 10 integers between 1 and 365 inclusive
Sequence[i = RandomBetween[1, 365], i, 1, 10]
4. Plot points from a ggb spreadsheet
Highlight the two columns you want to graph. Right click on your mouse or click on {1, 2} button. Select
Create – List of points
5. Statistical graphics of a data set.
Highlight the data. Click on the Histogram symbol. Select One Variable Analysis. Click on Analyze.
Choose Normal Quantile Plot (or Histogram, Dot Plot, Box Plot, Stem and Leaf Plot.) Click on ∑x to
get the statistics of the data set. To read the z-score of each datum, Click on the left arrow on the graph
screen and check the box Show Grid. The z-score is the y-axis.
6. To find Zα/2 , open the z-interval.ggb file. Check Two Tails button. Enter the value for  and n. Zα/2
the positive critical value.
7. To find the confidence Interval of a proportion: open a new ggb file. Click on the drop down menu
at the ABC symbol. Select Probability calculator. Choose Statitstics tab. Select Z Estimate of a
̂ is given, type in the Successes
Proportion. Enter the value for Confidence Level, Successes and N. If 𝒑
̂. GGB will compute this value.
box the value of N*𝒑
8. To find the confidence Interval of a mean (when σ is known): open a new ggb file. Click on the
drop down menu at the ABC symbol. Select Probability calculator. Choose Statitstics tab. Select Z
Estimate of a Mean. Enter the value for Confidence Level, Mean, σ and N.
9. To find tα/2: open the t-interval.ggb file. Check Two Tails button. Enter the value for  and n. tα/2
the positive critical value.
10. To find the confidence Interval of a mean (when σ is unknown): open a new ggb file. Click on the
drop down menu at the ABC symbol. Select Probability calculator. Choose Statitstics tab. Select T
Estimate of a mean. Enter the value for Confidence Level, Mean, s and N.
11. To find critical value for chi-square: open the chi-square Interval.ggb file. Check Two Tails
button. Enter the value for  and n.
12. To find the confidence Interval of a variance or standard deviation:
Open Chi-square Interval.ggb file. Check Two Tails option. Then enter values for , s and n.
If data are in the spreadsheet, check the Spreadsheet Data box, Enter the value for n.
13. Z-Test for a Proportion: open the z-test for one sample.ggb file. Select A proportion. Choose the
̂.
tail option. Enter the value for , n, p and 𝒑
14. Z-Test for a Mean (when σ is known): open the z-test for one sample.ggb file. Select A Mean.
Choose the tail option. Enter the value for , n, ,  and 𝑥̅ .
15. Z-Test for a Mean (when σ is unknown): open the t-test for one sample.ggb file. Choose the tail
option. Enter the value for , n, s,  and 𝑥̅ .
If data are in the spreadsheet, check the Spreadsheet Data box, Enter the value for n.
16. Chi-square Test for one sample:
Open Chi-square test for one sample.ggb. Choose the tail option. Then enter values for , s,  and n.
If data are in the spreadsheet, check the Spreadsheet Data box, Enter the value for n.
17. Z-Test for two proportions:
Open z-test for two proportions.ggb . Choose the tail option. Then enter values for , x and n.
18. T-Test for two independent samples:
Open t-test for two samples.ggb . Choose the tail option. Then type in values for , x , s and n.
If data are in the spreadsheet, check the Spreadsheet Data box, Enter the value for n.
19. T-Test for matched pairs
Open T-Test for one sample. On the spreadsheet screen, type the two samples in column B and C. For
each cell of Column A, type Bi –Ci for i = 1, 2, 3….
On the graphic screen, select Spreadsheet data, and enter the value for  and n. Then choose the tail
option.
20. Linear Correlation
Open Correlation Test. Select Spreadsheet Data. On the spreadsheet screen, type the two samples in
column A and B. Enter values for  and n. Choose Two tails. If r is given, uncheck Spreadsheet Data
and enter value of r on the graphic screen.
21. Regression Line
Open a new ggb file. On the spreadsheet screen, type the two samples in column A and B. Highlight the
two data sets. Click on the Histogram symbol. Select Two Variable Regression Analysis. Select Linear
to graphically estimate if there is a linear correlation.
To view the residue graph, on the Option menu, choose Show 2nd Plot.
22. Goodness-of-Fix Test
Open the Goodness-of-Fix.ggb file. On the spreadsheet, enter Observation values in column A and
Expected values in Column B. Enter value of k on the Graphing screen. Enter value for .
23. Homogeneity and Independence Test
Open the Goodness-of-Fix.ggb file. Check the Contingency Tables. On the spreadsheet, enter
Observation values in column A and Expected values in Column B. Enter value of , k (number of
categories), r (number of rows on Contingency Tables) and c (number of rows on Contingency Tables) on
the Graphing screen.
OR: Open a new ggb file. Click on View and select Spreadsheet. Click on any cell on Spreadsheet screen.
Click on the arrow on the Histogram symbol. Select Probability Calculator. Click on Statistics Tab. Click
on the drop down menu box, select ChiSquare Test. Choose the number of rows and columns. Type your
data into the table. Hit Enter after type the value for the last cell. You will see the result below the table.
24. One way ANOVA: Enter all data in the spreadsheet screen. Highlight all data. Click on the drop
down menu with the histogram symbol. Select Multiple Variable Analysis.
25. F-Test for Two Variances or Standard Deviations: Open F-test.ggb . Choose the tail option. Then
type in values for , s1, s2, n1, and n2.
26. Calculate the mean and standard deviation from a frequency table: Open the SD from freq
table.ggb. Enter value x on Column A and frequencies on Column B. Enter the number of row n on the
Graphic Screen. Hit Enter.
MATH 136 – PROJECT Lefty-Righty Experiment
Goals: Students will estimate the percentage of left-handed people around Glendale college and answer
the question “Why do some people write faster the other?”
PROJECT :
Each student has to give a survey of a group of at least 16 people. Students then will combine data with
their group of four students and apply the material in this course to analyze the group data. When
students have a group topic, please sign up on Moodle. Make sure your topic is not the same with any
topic posted on Moodle. To get 5pts, each group needs to sign up before 4/11/ 2015.
Project will be graded in three following categories: Sign-up: (5pts) Presentation (20pts),
Participation(20 pts), paper (group report:15 pts and individual report: 30 pts ), and Moodle post
(10pts).
Presentation: Students may use powerpoint in group presentation in five minutes or less. Make sure all
group data post on Moodle to get full credit.
Participation: Each student will get10 pts for posting survey data on Moodle by 11 pm 3/30/2015. The
other 10 points will put together as a group. Each group member will be graded based on how much
work s/he contributes to the group.
The group report must answer the followings:
Part 1: a. The scatterplot of the group data
b. From your group data, estimate the 95% confident interval for the percentage of left handed people in the
population. Use the result to test the claim that 10% of people are left handed. Remember to show all
your work. If you do not show the statistical process, you will not receive any credit for this section.
Part 2: a. Introduce your claim about the performance of your two group data. For example, are teacher faster
than students? Separate your data into two groups. Find the highest score of the left and right hand of each
person.
b. You then use the hypothesis testing to compare the performance the two groups. Use your group data and
follow the four steps of significance test to test your claim. Make sure to state what significance level you
used. Remember to show all your work. If you do not show the statistical process, you will not receive
any credit for this section.
Group reports must post on Moodle by 9 am 5/27/2015 to get full credit.
Your individual report must include the cover page and follow the format on the next page.
Final Project Requirements
Cover Page



Title
Your names
The rubric as seen below.
Math 136 –Project Name:
Sign up:_________/5
Moodle post: ______/10
Participation: ________/20
Presentation: ________/20
Paper: ________/45
Report:
Introduction
1. Provide an in depth description of your project, including clearly expressing what the data and
variables represent.
2. Include your research question, explain what the purpose of your project is and how you obtained
your information.
3. Explain in general the steps you are going to take and the statistical tools you are going to use to
answer your research question. Also explain what process you are going to use to reduce
confounding variables and bias.
Body
Part 1: Are 10% of people left-handed?
1. The graph of left & right hand marks to determine the number of left handed people.
2. Use the binomial distribution to see if the number of left handed people from your individual data is
unusual. If yes, describe the population of your survey to explain the nature of your data.
a. Estimate the 95% confidence interval for the percentage of left handed people and explain what the
interval range means. Use the result to test the claim that 10% of people are left handed. Explain any
different results between your data to your group data. If you do not show the statistical process, you
will not receive any credit for this section.
Part 2: Which group can write faster?
1. Separate your data into two groups. Find the highest score of the left and right hand of each person. Your
individual data unlikely meet the minimum requirement of 30 people. Test and see if you can use the
normal distribution. If your test fails, proceed and construct a confidence interval or hypothesis testing.
However, during your conclusion explain how your findings are not accurate since your distribution did
not follow normal distribution.
2. Conduct a Hypothesis Test about your claim. Explain the outcome based on the test. Make sure to
state what significance level you used. Explain any different results between your data to your group
data. Remember to show all your work. If you do not show the statistical process, you will not receive
any credit for this section.
Conclusion
1. State your research question again and explain your conclusion based on your research.
2. Illustrate any possible confounding variables or bias that could hinder your conclusion.
References
1. Provided all the resources you used for this project. It should be displayed in MLA form.