CMC3-SouthConference - Anaheim

March 14, 2015

A Visual path from Z to t to ANOVA

By: Tuyetdong Phan-Yamada– Glendale Community College

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GeoGebra Commands and Tests for Statistics

Download free GeoGebra at

All statistics files can be found at

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/2the 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. ChooseStatitsticstab. Select Z Estimate of a Proportion. Enter the value for Confidence Level, Successes and N. If is given, type in the Successes box the value of N*. GGB will compute this value.

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. ChooseStatitsticstab. Select Z Estimate of a Mean. Enter the value for Confidence Level, Mean, σ and N.

9. To findtα/2: open the t-interval.ggb file. Check Two Tails button. Enter the value for and n. tα/2the 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. ChooseStatitsticstab. Select T Estimate of a mean. Enter the value for Confidence Level, Mean, s and N.

11. To findcritical 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 aProportion: open the z-test for one sample.ggb file. Select A proportion. Choose the tail option. Enter the value for , n, p and .

14. Z-Test for aMean (whenσ is known): open the z-test for one sample.ggb file. Select A Mean. Choose the tail option. Enter the value for ,n, ,  and .

15. Z-Test for aMean (whenσ is unknown): open the t-test for one sample.ggb file. Choose the tail option. Enter the value for ,n, s,  and .

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, selectSpreadsheet 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, selectChiSquare 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, andn2.

26. Calculate the mean and standard deviation from a frequency table: Open the SD from freqtable.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 reportsmustpost 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.

  1. Estimate the 95% confidence intervalfor 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.

  1. 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.