[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-481941-105":3,"detail-sidebar-cat-0-en-105":80,"doc-detail-481941-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","examining-samples-solve-each-problem","Examining Samples - Solve Each Problem","","Practice problems use sampled survey data to make inferences. One scenario compares vote counts for two election candidates using sample results and asks what can be inferred about the likely winner. A second scenario estimates proportions of three types of canned vegetables from small samples and asks whether a meaningful conclusion can be drawn. A third scenario uses small samples of pizza topping preferences to decide which meat should be stocked most, testing the limits of inference from limited data.",{"@graph":14,"@context":72},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/examining-samples-solve-each-problem/481941/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/examining-samples-solve-each-problem/481941.png","ImageObject",300,407,{"name":42,"@type":43},"Alexandar","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-05","2026-09-30",true,{"@type":52,"interactionType":53,"userInteractionCount":33},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"How can the sample election results be used to infer the likely winner?","Question",{"text":62,"@type":63},"The sample indicates Candidate A has higher vote counts overall, so the election outcome can be inferred in favor of Candidate A.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"What conclusion can be drawn about the types of canned vegetables donated?",{"text":67,"@type":63},"Because the sample quantities differ only slightly, it is unlikely that a reliable deduction can be made about the overall types donated.",{"name":69,"@type":60,"acceptedAnswer":70},"Which meat topping should the pizzeria stock most based on the samples?",{"text":71,"@type":63},"With such small samples, it is impossible to make meaningful assumptions about which meat should be stocked most.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},481941,1792878033,{"code":4,"msg":81,"data":82},"success",[83,87,91,94,99,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":92,"slug":93},70,"exam",{"id":95,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},5,"Comic",60,"comic",{"id":100,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},6,"Technology",50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":95,"slug":129},19,"General","general",{"code":4,"msg":81,"data":131},{"doc_id":78,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":33,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":30,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":143,"read_time":110},962090768658,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Solve each problem.  \n1) During a class election a teacher wanted to predict who would win. To do this she took a sample of students from each class and asked who they would vote for. The results are shown below:  \n\n| \u003Cbr>Sample \\# | \u003Cbr>1 | \u003Cbr>2 | \u003Cbr>3 | \u003Cbr>4 | \u003Cbr>5 | \u003Cbr>6 | \u003Cbr>7 | \u003Cbr>8 |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| \u003Cbr>Candidate A | 59 | 61 | 62 | 61 | 61 | 59 | 59 | 59 |\n| \u003Cbr>Candidate B | 52 | 50 | 52 | 52 | 52 | 52 | 50 | 52 |\n\nBased on the information presented can you infer anything about who will win the election?  \nBased on the information presented Candidate A will have 14% more votes.  \n2) For a canned food drive there were 3 types of cans vegetables donated: peas, carrots and green beans. To estimate how many of each type were donated, you pull out a sample. The results are shown below:  \n\n| \u003Cbr>Sample \\# | \u003Cbr>1 | \u003Cbr>2 | \u003Cbr>3 | \u003Cbr>4 | \u003Cbr>5 |\n| --- | --- | --- | --- | --- | --- |\n| \u003Cbr>peas | 31 | 31 | 29 | 31 | 30 |\n| \u003Cbr>carrots | 29 | 31 | 31 | 32 | 32 |\n| \u003Cbr>green beans | 31 | 29 | 32 | 30 | 32 |\n\nBased on the information presented can you infer anything about the types of cans donated?  \nBecause of the very small discrepancy in the quantities it is unlikely any deduction can be made about the types of cans donated.  \n3) A pizzeria owner was trying to determine which types of meat he should stock the most of for his new store. To do this he asked several pizza eaters what their favorite toppings were. His results are shown below:  \n\n| \u003Cbr>Sample \\# | \u003Cbr>1 | \u003Cbr>2 | \u003Cbr>3 | \u003Cbr>4 | \u003Cbr>5 |\n| --- | --- | --- | --- | --- | --- |\n| \u003Cbr>Pepperoni | 1 | 1 | 2 | 3 | 4 |\n| \u003Cbr>Sausage | 4 | 3 | 3 | 2 | 0 |\n| \u003Cbr>Ham | 0 | 3 | 3 | 2 | 1 |\n\nBased on the information presented what can you infer about which type of meat he should stock?  \nBased on the information presented and the small samples gathered it is impossible to make any meaningful assumptions.  \nSolve each problem.  \n1) During a class election a teacher wanted to predict who would win. To do this she took a sample of students from each class and asked who they would vote for. The results are shown below:  \n\n| \u003Cbr>Sample \\# | \u003Cbr>1 | \u003Cbr>2 | \u003Cbr>3 | \u003Cbr>4 | \u003Cbr>5 | \u003Cbr>6 | \u003Cbr>7 | \u003Cbr>8 |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| \u003Cbr>Candidate A | 59 | 61 | 62 | 61 | 61 | 59 | 59 | 59 |\n| \u003Cbr>Candidate B | 52 | 50 | 52 | 52 | 52 | 52 | 50 | 52 |\n\nBased on the information presented can you infer anything about who will win the election?  \nBased on the information presented Candidate A will have 14% more votes.  \n2) For a canned food drive there were 3 types of cans vegetables donated: peas, carrots and green beans. To estimate how many of each type were donated, you pull out a sample. The results are shown below:  \n\n| \u003Cbr>Sample \\# | \u003Cbr>1 | \u003Cbr>2 | \u003Cbr>3 | \u003Cbr>4 | \u003Cbr>5 |\n| --- | --- | --- | --- | --- | --- |\n| \u003Cbr>peas | 31 | 31 | 29 | 31 | 30 |\n| \u003Cbr>carrots | 29 | 31 | 31 | 32 | 32 |\n| \u003Cbr>green beans | 31 | 29 | 32 | 30 | 32 |\n\nBased on the information presented can you infer anything about the types of cans donated?  \nBecause of the very small discrepancy in the quantities it is unlikely any deduction can be made about the types of cans donated.  \n3) A pizzeria owner was trying to determine which types of meat he should stock the most of for his new store. To do this he asked several pizza eaters what their favorite toppings were. His results are shown below:  \n\n| \u003Cbr>Sample \\# | \u003Cbr>1 | \u003Cbr>2 | \u003Cbr>3 | \u003Cbr>4 | \u003Cbr>5 |\n| --- | --- | --- | --- | --- | --- |\n| \u003Cbr>Pepperoni | 1 | 1 | 2 | 3 | 4 |\n| \u003Cbr>Sausage | 4 | 3 | 3 | 2 | 0 |\n| \u003Cbr>Ham | 0 | 3 | 3 | 2 | 1 |\n\nBased on the information presented what can you infer about which type of meat he should stock?  \nBased on the information presented and the small samples gathered it is impossible to make any meaningful assumptions.  \nSolve each problem.  \n1) During a class election a teacher wanted to predict who would win. To do this she took a sample of ","cbCain3DtAOxKrWs","https://ap.wps.com/l/cbCain3DtAOxKrWs","pdf",90374,"English","# Election and sample inference\n# Canned food drive proportions\n# Pizza topping preference sampling","[{\"question\":\"How can the sample election results be used to infer the likely winner?\",\"answer\":\"The sample indicates Candidate A has higher vote counts overall, so the election outcome can be inferred in favor of Candidate A.\"},{\"question\":\"What conclusion can be drawn about the types of canned vegetables donated?\",\"answer\":\"Because the sample quantities differ only slightly, it is unlikely that a reliable deduction can be made about the overall types donated.\"},{\"question\":\"Which meat topping should the pizzeria stock most based on the samples?\",\"answer\":\"With such small samples, it is impossible to make meaningful assumptions about which meat should be stocked most.\"}]","Examining Samples - Solve Each Problem | PDF",1790797733]