[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-399215-105":59,"doc-detail-399215-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","stat-400-week-14-discussion-fall-2017","STAT 400 Week 14 Discussion - Fall 2017","","Discussion notes for STAT 400 Week 14 (Fall 2017) covering multiple hypothesis-testing and confidence-interval problems in actuarial and biostatistical contexts. Topics include building a 95% confidence interval for a pass proportion, determining minimum sample size for margin-of-error requirements, and conducting two-proportion comparisons with p-values. Additional sections address weight comparisons between adult animals using equal-variance, Welch, and conservative approaches, plus paired t testing for pulse-rate changes before and after a stimulus. Also included are tests comparing teacher starting salaries across private and public schools, with both one-sided and two-sided alternatives.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/stat-400-week-14-discussion-fall-2017/399215/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/stat-400-week-14-discussion-fall-2017/399215.png","ImageObject",300,407,{"name":92,"@type":93},"McQueen","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-31","2026-09-27",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you construct a 95% confidence interval for the overall proportion of students passing Exam P in 2017?","Question",{"text":113,"@type":114},"Use the sample pass proportion p-hat based on 74 passed out of 200, then apply a normal-based (z) proportion confidence interval at 95% confidence.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What test and confidence approach should be used for the rhino versus hippo weight difference when variances may not be equal?",{"text":118,"@type":114},"When not assuming equal variances, use Welch’s t for confidence intervals and hypothesis testing; if taking a conservative approach, do not rely on the equal-variance assumption.",{"name":120,"@type":111,"acceptedAnswer":121},"How is the pulse-rate effect tested using the paired t test?",{"text":122,"@type":114},"Compute differences between each child’s after and before pulse rates, then perform a two-sided paired t test at α = 0.05 to assess whether the mean difference is nonzero.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},399215,1791189830,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":145,"read_time":146,"preview_page_count":4},5909890329169,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","STAT 400 Week 14 Discussion Fall 2017  \n1. In a random sample of 200 students who took Exam P in 2017, 74 successfully passed the exam. ( Exam P [ Probability ] is the first Actuarial Science exam. )  \na) Construct a 95% confidence interval for the overall proportion of students who successfully passed Exam P in 2017.  \nb) Find the minimum sample size required for estimating the overall proportion of  \nstudents who passed Exam P in 2017 to within 4% with 95% confidence if it is known that this proportion is between 30% and 40% .  \nc) In 2016, the success rate on Exam P was 41% . At a 10% level of significance, test whether the success rate on Exam P in 2017 has changed from 2016. Find the p-value of this test.  \n1. (continued)  \nSuppose also that in a random sample of 150 students who took Exam FM in 2017, 45 successfully passed the exam. ( Exam FM [ Financial Mathematics ] is the second Actuarial Science exam. )  \nd) Construct a 95% confidence interval for the difference between the overall proportions of students who passed Exam P and Exam FM in 2017.  \ne) At a 10% level of significance, test whether Exam P had a higher success rate than Exam FM in 2017. Find the p-value of this test.  \n2. A random sample of 9 adult white rhinos had the sample mean weight of 5,100 pounds and the sample standard deviation of 450 pounds. A random sample of 16 adult hippos had the sample mean weight of 3,300 pounds and the sample standard deviation of 400 pounds. Assume that the two populations are approximately normally distributed.  \na) Construct a 95% confidence interval for the difference between their overall average weights of adult white rhinos and adult hippos.  \ni) Assume that the overall standard deviations are equal.  \nii) Do NOT assume that the overall standard deviations are equal. Use Welch’s T.  \niii) Do NOT assume that the overall standard deviations are equal. Use conservative approach.  \nb) Test H 0 : 􀁐 R – 􀁐H = 1,500 vs. H 1 : 􀁐 R – 􀁐H > 1,500 at 􀁄 = 0.05.  \ni) Assume that the overall standard deviations are equal.  \nii) Do NOT assume that the overall standard deviations are equal. Use Welch’s T.  \n3. In a random sample of eight 8-to-12-year-old children, the sample mean time playing video games was 48.8 hours per month with sample standard deviation 3.5 hours. In a random sample often 13-to-18-year-olds, the sample mean time playing video games was 54.3 hours per month with sample standard deviation 5.3 hours. Assume that the two populations are normally distributed.  \na) Assume that the two population variances are equal. Construct a 95% confidence interval for the difference between are average time 8-to-12-year-olds and 13-to-18-year-olds play video games per month.  \nb) Since the larger sample variance is more than twice as big as the smaller one, the assumption of equal variances is questionable here. Construct a 95% confidence interval for the difference between are average time 8-to-12-year-olds and 13-to-18-year-olds play video games per month without assuming that the two population variances are equal. Use Welch’s T.  \n4. A researcher wishes to determine whether the starting salaries of high-school math teachers in private schools are higher than those of high-school math teachers in public schools. She selects a sample of new math teachers from each type of school and calculates the sample means and sample standard deviations oftheir salaries.  \n\n|  | Private | Public |\n| --- | --- | --- |\n| sample size | 10 | 7 |\n| sample mean | $36,800 | $36,300 |\n| sample standard deviation | $600 | $546 |\n\nAssume that the populations are normally distributed and the population variances are equal.  \na) Construct a 95% confidence interval for the difference in average starting salaries of high-school math teachers in private and public schools.  \nb) Perform the appropriate test at a 1% level of significance. That is, test H 0 : 􀁐 Private = 􀁐 Public vs. H 1 : 􀁐 Private > 􀁐 Public .  \nc) Find the p-value of the test in part (b) .","cbCaifRac2sSO4VG","https://ap.wps.com/l/cbCaifRac2sSO4VG","pdf",192566,13,"English","# Exam P: Confidence interval, sample size, and proportion change\n## Exam P vs Exam FM: Difference and higher-success test\n# Weight comparisons: Rhinos vs hippos\n## Equal variances, Welch’s t, and conservative approach\n# Video game time comparison: children vs adolescents\n## Equal variances and unequal variances (Welch’s t)\n# Starting salaries: private vs public high-school math teachers\n## Confidence interval and hypothesis tests (one-sided and two-sided)\n# Paired t test: pulse rate before vs after a violent movie","[{\"question\":\"How do you construct a 95% confidence interval for the overall proportion of students passing Exam P in 2017?\",\"answer\":\"Use the sample pass proportion p-hat based on 74 passed out of 200, then apply a normal-based (z) proportion confidence interval at 95% confidence.\"},{\"question\":\"What test and confidence approach should be used for the rhino versus hippo weight difference when variances may not be equal?\",\"answer\":\"When not assuming equal variances, use Welch’s t for confidence intervals and hypothesis testing; if taking a conservative approach, do not rely on the equal-variance assumption.\"},{\"question\":\"How is the pulse-rate effect tested using the paired t test?\",\"answer\":\"Compute differences between each child’s after and before pulse rates, then perform a two-sided paired t test at α = 0.05 to assess whether the mean difference is nonzero.\"}]","STAT 400 Week 14 Discussion - Fall 2017 | PDF",1790494837,33]