Running head: MAT 223 FINAL PROJECT 1 MAT 223 Final Project: Exploring the Class Data Spring 2016 Henry M. Flagler Flagler College MAT 223 FINAL PROJECT 2 MAT 223 Final Project: Exploring the Class Data Spring 2016 In this section, you will need to state the purpose of the study, explain the importance of the research, and what you expected to find in your sample data. SUMMARY OF DATA COLLECTION Identify your sample and the targeted population. State any bias that may exist in your data based on your surveying technique. List the survey questions, but not the answers. SUMMARY OF SAMPLE DATA - GRAPHS AND STATISTICS Demographics First describe your sample in regards to demographics. The first demographic is gender. Include a written paragraph description of the categorical distribution in complete sentences. Recall, use the percent and not the count to describe your sample. Include in the description the two components: (1) Mode and (2) Variability. The second demographic is age. Include a written paragraph description of the numerical distribution in complete sentences. Include in the description the four components: (1) Shape, (2) Best measure of Center, (3) Best measure of Variability, and (4) Outliers. Summary statistics: Column n Age Mean 78 18.769231 Median Mode Min Max Range IQR Std. dev. 18 18 17 28 11 1 1.528288 Interesting Sample Results IN THIS LOCATION, YOU WILL HAVE AT LEAST SIX MORE GRAPHS; FOUR FOR CATEGORICAL VARIABLES AND TWO FOR NUMERICAL VARIABLES. YOU MUST USE MAT 223 FINAL PROJECT 3 THE SAME FORMAT AS OUTLINED FOR GENDER AND AGE GIVEN ABOVE FOR THESE SIX OTHERS GRAPHS YOU CREATE! PLEASE SELECT DATA THAT IS INTERESTING TO THE READER AND IMPORTANT TO YOUR STUDY. IN PARTICULAR, IN THIS TEMPLATE, A GRAPH REPRESENTING THE STUDENT RESPONSES TO \"SHOULD SMOKING BE ALLOWED IN THE GAZEBO\" WOULD BE INCLUDED BECAUSE A TEST TO DETERMINE IF THE MAJORITY OF ALL STUDENTS DO NOT WANT SMOKING PREMITTED IN THE GAZEBO IS RUN IN PART VI. SOME OF YOUR PAPERS MAY NEED TO GO FURTHER INTO THE DEMOGRAPHICS OF THE SAMPLE (IE. ACADEMIC STANDING, LIVE ON OR OFF CAMPUS, ETC.) PLEASE INCLUDE THIS INFORMATION ONLY IF IT RELEVANT TO YOUR STUDY! Interesting Sample Results between Groups Compare the results of one numerical variable to your study. Include a written paragraph description of between groups that is important the numerical distribution in complete sentences. Include in the description the four components: (1) Shape, (2) Five (4) Outliers. Also, include a written paragraph distributions in regards to their relationship between identified in the stacked boxplots. Summary statistics for Rich: Group by: Gender Number Summary, (3) IQR, and comparing the two each other as MAT 223 FINAL PROJECT 4 Gender n Female 38 Male Min Q1 Median Q3 Max IQR 300 100000 100000 300000 1000000 200000 18 10000 100000 275000 500000 2000000 400000 ASSOCIATIONS BETWEEN VARIABLES Contingency Table: Exploring Associations in Categorical Variables Compare the association between two different pairs of two categorical variables that has importance to your study. Calculate the necessary probabilities to determine if there exists an association between the categorical variables. Write a paragraph description of the association in complete sentences. Include in the description if the variables (events) are independent or dependent. Please explain your reasoning based on the calculated probabilities. Contingency table results: Rows: Negative Columns: Employer Rights No; an employer does not Yes; an employer does have Total have the right to look up a the right to look up a potential employee on social potential employee on social media. media. No; nothing negative has ever occurred to me based on a social media post. 9 36 45 Yes; something negative has occurred to me based on a social media post. 10 17 27 Total 19 53 72 YOU WILL NEED TWO COMPARISONS FOR TWO DIFFERENT PAIRS OF CATEGORICAL DATA. PLEASE INCLUDE THE CONTINGENCY TABLE FOR BOTH COMPARISONS AND AN EXPLANATION FOR BOTH COMPARISONS. MAT 223 FINAL PROJECT 5 STATISTICAL INFERENCE Hypothesis Test #1 - A Claim of Majority The first hypothesis test deals with categorical data and will test a claim of majority. In the example here, the claim is that the majority of Flagler College students do not want smoking to be permitted in the Gazebo. Write a paragraph in complete sentences that introduces your hypothesis test. Please include in the introduction the null and alternate hypothesis in words and the level of significance (typically = 0.05), state if the test is right, left, or two tailed, and reference the graph associated with the test. Then, check the necessary conditions. One sample proportion hypothesis test: Outcomes in : Gazebo Success : No p : Proportion of successes H0 : p = 0.5 HA : p > 0.5 Hypothesis test results: Variable Count Total Sample Prop. Gazebo 44 74 Std. Err. Z-Stat 0.59459459 0.058123819 1.6274669 P-value 0.0518 After running the test, make a statement in regards to rejecting or failing to reject the null hypothesis. Finally state a conclusion. Your conclusion always refers back to the statement of the claim. Confidence Interval #1 - Estimating the Population Proportion The first confidence interval is associated with the first hypothesis test. Regardless of your test results, it is always good to estimate the population proportion using a confidence MAT 223 FINAL PROJECT 6 interval. Write a paragraph in complete sentences that introduces the confidence interval you plan to construct identifying the level of significance you plan to use. Next, check the necessary conditions. One sample proportion confidence interval: Outcomes in : Gazebo Success : No p : Proportion of successes Method: Standard-Wald 90% confidence interval results: Variable Count Total Sample Prop. Gazebo 44 74 Std. Err. L. Limit U. Limit 0.59459459 0.057074141 0.50071599 0.6884732 After running the confidence interval, write a complete sentence explaining the confidence interval and what it estimates. Hypothesis Test #2 - A Claim of the Difference between two Population Proportions The second hypothesis test deals with categorical data and will test a claim of a difference between two population proportions. A contingency table for your claim must be included as one of your tables in section ASSOCIATIONS BETWEEN VARIABLES. In the example here, the claim is that there is a greater percentage of Flagler College students who support employer rights to look up a potential employee on social media among those students who have not had a negative experience due to a social media post as compared to those students who have had a negative experience due to a social media post. Therefore, the two different populations are \"Flagler College students with negative online experience\" and \"Flagler College students without negative online experience\" and the variable is \"Support employer rights.\" MAT 223 FINAL PROJECT 7 Write a paragraph in complete sentences that introduces your hypothesis test. Please include in the introduction the null and alternate hypothesis in words and the level of significance (typically = 0.05), state if the test is right, left, or two tailed, and reference the graph associated with the test. Then, check the necessary conditions. Two sample proportion hypothesis test: p1 : Proportion of successes (Success = Yes) for Employer Rights where Negative = "No" p2 : Proportion of successes (Success = Yes) for Employer Rights where Negative = "Yes" p1 - p2 : Difference in proportions H0 : p1 - p2 = 0 HA : p1 - p2 > 0 Hypothesis test results: Difference Count1 Total1 Count2 Total2 p1 - p2 36 45 17 Sample Diff. Std. Err. Z-Stat Pvalue 27 0.17037037 0.10729027 1.5879386 0.0562 After running the test, make a statement in regards to rejecting or failing to reject the null hypothesis. Finally state a conclusion. Your conclusion always refers back to the statement of the claim. Confidence Interval #2 -Estimate the Difference between two Population Proportions The second confidence interval deals with categorical data and estimate the difference between two population proportions. Regardless of your test results, it is always good to estimate the population proportion using a confidence interval. Write a paragraph in complete sentences that introduces the confidence interval you plan to construct identifying the level of significance you plan to use. Next, check the necessary conditions. Two sample proportion confidence interval: p1 : Proportion of successes (Success = Yes) for Employer Rights where Negative = "No" p2 : Proportion of successes (Success = Yes) for Employer Rights where Negative = "Yes" p1 - p2 : Difference in proportions 90% confidence interval results: MAT 223 FINAL PROJECT 8 Difference Count1 Total1 Count2 Total2 p1 - p2 36 45 17 Sample Diff. Std. Err. 27 0.17037037 0.11041943 L. Limit U. Limit -0.0112534 0.35199417 After running the confidence interval, write a complete sentence explaining the confidence interval and what it estimates. CONCLUSION The conclusion given here is an overall conclusion/reflection to what you found. The conclusion is short and to the point. If a recommendation needs to be made based on your research, this is the location where the recommendation should be made. Furthermore, recommendations for redesigning the study should also be included here