MATH 339 QUIZ COARSE TEST ANSWERS AVAILABLE

Introduction MATH 339 QUIZ COARSE TEST ANSWERS AVAILABLE The topic that I have chosen is the graduation rates of US high schools for the year (“High School Graduation Rates by State 2019”, 2019). The data is found from World Population Review and lists the graduation rates as a percentage for each state. Only public schools are considered within the data as information from private schools are not accessible since they are not run by the government. Sample Data 89.3 78.2 78 88 82.7 79.1 87.9 86.9 82.3 80.6 82.7 79.7 87 83.8 91 86.5 89.7 78.1 86.9 87.7 88.3 80.2 82.7 83 88.3 85.8 89.1 80.9 88.9 90.5 71.1 81.8 86.6 87.2 84.2 82.6 76.7 86.6 84.1 83.6 83.7 89.8 89.7 86 89.1 86.9 79.4 89.4 88.6 86.2 Table 1. Graduation Rate Data Set in All Fifty States [1] Problem Computations Mean μ= 89.3+78.2+…+ 86.2=84.6 50 Standard Deviation √ Confidence Intervals and Margin of Error 80% zc=1.28 E= zc∗σ =1.28∗4.27 =0.773 ≈ 0.77 √n √50 upper limit =μ+ E=84.6+ 0.77=85.37 lower limit= 84.6−0.77=83.83 confidence interval =[ 83.83,85 .37] 95% zc=1.96 E= 1.96∗4.27 =1.183≈ 1.18 √50 upper limit =84.6+ 1.18=85.78 lower limit=84.6−1.18=83.40 confidence interval =[ 83.40,85 .78] 99% zc=2.575 E= 2.575∗4.27 =1.55496 ≈ 1.55 √50 upper limit =84.6+ 1.55=86.15 lower limit=84.6−1.55=83.01 confidence interval =[ 83.01,86 .15] 90% (chosen confidence interval) zc=1.645 E= 1.645∗4.27 =0.99 √50 upper limit =84.6+ 0.99=85.5 lower limit=84.6−0.99=83.5 confidence interval =[ 83.5,85 .5] Problem Analysis What trend do you see takes place to the confidence interval as the confidence level rises? Explain mathematically why that takes place. As the confidence interval rises, the upper limit gets bigger and the lower limit becomes smaller. It is expected to see this observation mostly due to the level of confidence increasing. The bigger the difference between the upper and lower limits, the more confident we are in predicting that the value is within those bounded limits. Provide a sentence for each confidence interval created in part c) which explains what the confidence interval means in context of topic of your project. With a confidence interval of 80%, we are 80% confident that the average graduation rate within a sample of US public high schools is between 83.83% and 85.37%. With a confidence interval of 95%, we are 95% confident that the average graduation rate within a sample of US public high schools is between 83.40% and 85.78%. With a confidence interval of 99%, we are 99% confident that the average graduation rate within a sample of US public high schools is between 83.01% and 86.15%. With a confidence interval of 90%, we are 90% confident that the average graduation rate within a sample of US public high schools is between 83.5% and 85.5%. Explain how Part I of the project has helped you understand confidence intervals better? This helped me understand the topic of confidence interval much better by giving me the opportunity to do calculations on an example data set. Calculating the upper and lower limits for each confidence interval and comparing each interval allowed me to understand what it means with regards to its context. How did this project help you understand statistics better? In this project, I was able to analyze the outcomes of the calculations and understand its overall significance with regards to the topic. The calculations gave me a better understanding of the data set, which is one of the objectives of statistics. Course Project 2 Chosen Data Set Volume 58. Number 22. Release Date: July 9, 2009. Column: October 2009 Preliminary Calculations Summary Table for Live Births Mean 6754 Median 4643 Standard Deviation 8819.19 Minimum 519 Maximum 46661 Summary Table for Deaths Mean 4001 Median 2961 Standard Deviation 3986.42 Minimum 278 Maximum 19319 Summary Table for Marriages Mean 3801 Median 3000 Standard Deviation 3487.41 Minimum 270 Maximum 16447 Summary Table for Divorces Mean 1582 Median 1274 Standard Deviation 1395.59 Minimum 30 Maximum 7008 Hypothesis Testing a. Ho : M ≤ 5000 Ha : M >5000 (claim) α =0.05 z= 6754−5000 =1.56 8119.19/ √52 P=1−0.9406=0.0594 P>α Conclusion: Fail to reject null hypothesis H0. At the 5% significance level, there is not sufficient evidence to conclude that the average amount of live births is over 5000. b. Ho : M =6000( claim) Ha : M ≠ 6000 α =0.10 z= 4001−6000 =−3.62 3986.42/ √52 P=2 (0.05)=0.1 P≤α Conclusion: Reject null hypothesis H0. At the 10% significance level, there is not sufficient evidence to conclude that the average amount of deaths is 6000. c. Ho : M ≥ 2500(claim ) Ha : M ∈2500 α =0.05 z= 3801−2500 =2.69 3487.41/ √52 P=0.9964 P>α Conclusion: Fail to reject null hypothesis H0. At the 5% significance level, there is sufficient evidence to conclude that the average amount of marriages is greater than or equal to 2500. d. Ho : M ≤ 4000( claim) Ha : M > 4000 α =0.10 z= 1582−4000 =−11.75 1395.59/ √46 P=1 P>α Conclusion: Fail to reject null hypothesis H0. At the 10% level of significance, there is sufficient evidence to conclude that the average amount of divorces is less than or equal to 4000. e. My own hypothesis: Determine if there is enough evidence to conclude that the average amount of divorces is less than 3000 in the United States and territories at a level of confidence of 0.10. Ho : M ≥ 3000 Ha : M ∈3000 (claim) α =0.10 z= 1582−3000 =−6.89 1395.59/ √46 P=0 P≤α Conclusion: Reject null hypothesis H0. At the 10% level of significance, there is sufficient evidence to conclude that the average amount of divorces is less than 3000. References 1. High School Graduation Rates by State 2019. (n.d.). Retrieved December 8, 2019, from 2. Centers for Disease Control and Prevention, National Health Statistics Reports. (2010). National health statistics reports: Births, Marriages, Divorces, and Deaths: Provisional Data for October, 2009 (Report No. 22). Retrieved from