MATH 1342 Project The Titanic was a mighty passenger ship. It was the largest ship afloat at the time she entered service. During her maiden voyage, she struck an iceberg on April 15, 1912 and sank....

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MATH 1342 Project The Titanic was a mighty passenger ship. It was the largest ship afloat at the time she entered service. During her maiden voyage, she struck an iceberg on April 15, 1912 and sank. You are going use a data set for the whole population of individuals who were aboard the Titanic at the time she sank. The variables are: • Class: whether the individual was first-class passenger, second-class passenger, third-class passenger or crew member. • Age: adult or child. • Gender: male or female. • Survived: yes or no. The population data set can be found under the content area “Project” on Blackboard. I will also provide each of you who choose to do the project with a random sample of data from the population. Email me indicating that you plan to do the project, and I will send the csv file containing your sample data set. You will use both data files in your analyses. You will use the sample data set to do the confidence intervals and hypothesis tests including the test. Copy all of the questions from this document and paste them into your report. Type your answers and paste relevant graphs and StatKey output after each question. You will lose a substantial number of points if you don’t submit all of the output you used. 1. How many individuals are in the population? 2. How many individuals are in your sample? 3. List the variables and indicate whether they are quantitative or categorical. Survival 4. Make a bar chart for the distribution of the variable survival in the population. 5. What proportion of the individuals in the population survived? Use correct notation. 6. What proportion of individuals in your sample survived? Use correct notation. 7. Find 95% and 99% confidence intervals for the parameter using the sample data set and a bootstrap distribution. 8. Interpret the two confidence intervals in context. 9. Do the intervals capture the true value of the parameter? 10. Are the conditions met in order to use the sample data set and the normal distribution to find a 95% and 99% confidence intervals? Justify your answer. 11. If you answered yes to 10, find the two confidence intervals. Show all of your computational work. 12. How do the intervals found from the bootstrap and the normal distribution compare? Do they yield similar results? Answer only if you answered yes to 10. Next, you are going to use our sample to investigate a claim about the population. Specifically you are going to investigate whether there is evidence from your sample that the true survival rate is more than 25%. 13. State the null and alternative hypotheses. 14. Use the sample data set and a randomization distribution to conduct the hypothesis test. Attach the output. 15. State your conclusion in context. 16. Are the conditions met in order to use the sample data set and the normal distribution to conduct the hypothesis test? Justify your answer. 17. If you answered yes to the 16, run the test with the sample data set and the normal distribution showing all of the steps. Association of Survival with Class Now, you are going to investigate whether the variable survival is associated with class. 18. Write the appropriate null and alternative hypotheses. 19. Carry out the test with a randomization distribution. 20. Write Part I of your conclusion. 21. Using the sample data set and the Descriptive Statistics and Graphs section in Statkey, generate the appropriate side-by-side bar chart. 22. Using the side-by-side bar chart and detailed sample table from the test for association as a guide, write Part II of your conclusion. 23. Are the conditions met in order to use the sample data set and the theoretical distribution and the sample data set to conduct the hypothesis? Justify your answer with reference to output from Statkey. If the conditions are met, find the p-value for the test with the theoretical distribution. Difference in Proportions Now you are going to investigate whether the survival rate differs between first-class passengers and third-class passengers. 24. What is correct notation for the parameter? 25. What is the value of the best estimate for the parameter? Use correct notation. 26. Create 95% and 99% confidence intervals using the sample data set and a bootstrap distribution. 27. Interpret the intervals in context. 28. What is the true value for the parameter? Use correct notation. 29. For each interval, indicate whether it captures the true value of the parameter. 30. Are the conditions met in order to use the sample data set and the normal distribution to construct 95% and 99% confidence intervals? Justify your answer. 31. If you answered yes to 30, carry out the computations using the sample data set showing your work. 32. Next, you are going to investigate whether there is evidence for the claim that the survival rate is lower for third-class passengers than for first-class passengers. State the appropriate hypotheses. 33. Use the sample data set and a randomization distribution to run the test at the level. 34. Write a conclusion in context. 35. What is the true value for the parameter? Use correct notation. 36. Are the conditions met for using the sample data set and the normal distribution for running the hypothesis test? Justify your answer. 37. If your answer to 36 was yes, conduct the test using the sample data set and the normal distribution showing all steps.