[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-506379-en":3,"detail-sidebar-cat-0-en-105":31,"doc-seo-506379-105":80},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30,"preview_page_count":4},506379,687207024478,"Mia  ","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",4,"Exam","Statistics - Hypothesis Testing - Handout","A hypothesis testing handout explains how to evaluate claims about a population using sample data. It defines the null and alternative hypotheses, distinguishes right-tailed, left-tailed, and two-tailed tests, and introduces rejection regions via critical values. The guide details how to compute a test statistic (z or t) by matching formulas to parameters such as known or unknown variance, and it outlines the full P-value and decision procedure.","Statistics: Hypothesis Testing  \nA hypothesis is a claim made about a population. A hypothesis test uses sample data to test the validity of the claim. This handout will define the basic elements of hypothesis testing and provide the steps to perform hypothesis tests using the P-value method and the critical value method. Many statistics courses use statistical calculation tools; however, this handout is designed for manually computed formulas.  \nBasics of Hypothesis Testing  \nAll hypothesis tests consist of a null hypothesis (H0) and an alternative hypothesis, which can be noted as HA, Ha, or H1. The null hypothesis must be written with an equality ( =, ≤, or ≥), and the alternative hypothesis must be written with an inequality (\u003C, >, or ≠) . Based on the inequality sign in the alternative hypothesis, there are three types of tests: right-tailed test (>), left-tailed test (\u003C), and two-tailed test (≠) . Below are diagrams of the three possible tests represented as distribution curves:  \nRight-tailed  \nTwo-tailed  \nThe shaded area of the graph represents the rejection region. The critical value is the z or t score that separates the rejection region from the fail to reject region.  \nTest Statistic  \nA test statistic is used to decide whether to reject or fail to reject the null hypothesis. It converts the sample statistic (proportion, p̂ or mean, x̅) to a score (z or t) by comparing the sample statistic to the null hypothesis. The test statistic that is used is dependent upon the parameter (mean, µ or proportion, p) being tested and whether the population standard Provided by Statistics: Hypothesis Testing  \ndeviation (σ) is known. Refer to the following table for formulas when deciding which test statistic is required for a given problem. Always remember to check the requirements.  \n\n| Sampling\u003Cbr>Distribution | Requirements | Formula | StatCrunch |\n| --- | --- | --- | --- |\n| Normal Distribution (z)\u003Cbr>for mean | 1. σ is known\u003Cbr>2. Normal distribution or\u003Cbr>n > 30 | z = -nμ x̅ = Sample mean µ = Population mean σ = Population standard deviation n = Sample size | 1. Stat > Z stats > one sample\u003Cbr>2. Choose with data or with summary\u003Cbr>3. Perform:\u003Cbr>Hypothesis test\u003Cbr>4. Compute |\n| t Distribution\u003Cbr>for mean | 1. σ is unknown\u003Cbr>2. Normal distribution or\u003Cbr>n > 30 | t = -~~s~~nμ x̅ = Sample mean µ = Population means = Sample standard deviation\u003Cbr>n = Sample size | 1. Stat > T stats > one sample\u003Cbr>2. Choose with data or with summary\u003Cbr>3. Perform:\u003Cbr>Hypothesis test\u003Cbr>4. Compute |\n| Normal Distribution (z) for proportion | [1.](1. np)[ np](1. np) ≥ 5\u003Cbr>2. n (1 − p) ≥ 5 *\u003Cbr>*some sources use q instead of (1-p) | p̂ -p z = ~~  ~~\u003Cbr>√p(1~~n~~-p) p̂ = Sample proportion p = Population proportion n = Sample size | 1. Stat > Proportion stats > one sample\u003Cbr>2. Choose with data or with summary\u003Cbr>3. Perform:\u003Cbr>Hypothesis test\u003Cbr>4. Compute |\n\nSignificance Level (α)  \nThe significance level is the probability value that is used to determine the cutoff for significant evidence against the null hypothesis. Typical significance levels are .05 and .01. The level will be given in the problem.  \nHypothesis Testing Steps  \nStep 1: Identify the claim and express in symbolic form.  \nStep 2: Write the null and alternative hypothesis.  \nStep 3: Calculate the test statistic.  \nStep 4: Find the P-value or critical value.  \nStep 5: Decide to reject or not to reject.  \nStep 6: Make a statement regarding the validity of the claim in the hypothesis test.  \nExample 1:  \nA study in 2000 found that 85 out of 100 Virginia residents own a dog. A simple random sample of 2500 people from Virginia was gathered, and the proportion of people who own a dog was found to be 0.84. Perform a hypothesis test at the 0.05 significance level (α) to test the claim that the proportion of dog owners in Virginia is now less than 85% .  \nStep 1: Identify the claim and express in symbolic form  \nWhen determining the claim, look for the sentence containing inequality keyw","cbCaihrIXNm1wtc8","https://ap.wps.com/l/cbCaihrIXNm1wtc8","pdf",516538,8,1,7,"English","en",105,"# Basics of Hypothesis Testing\n## Null and Alternative Hypotheses\n## Types of Tests (Right, Left, Two-Tailed)\n# Test Statistic and Rejection Region\n## Critical Values (z or t)\n# Selecting the Correct Test Formula\n## Mean with Normal Distribution (z)\n## Mean with t Distribution\n## Proportion with Normal Distribution (z)\n# Significance Level (α)\n# Hypothesis Testing Steps\n## Example Walkthrough for a Proportion Test","[{\"question\":\"What is the difference between the null hypothesis and the alternative hypothesis?\",\"answer\":\"The null hypothesis (H0) is written with equality (e.g., =, ≤, or ≥). The alternative hypothesis (HA, Ha, or H1) is written with an inequality (\\u003c, \\u003e, or ≠).\"},{\"question\":\"How do you determine whether a test is right-tailed, left-tailed, or two-tailed?\",\"answer\":\"Use the inequality sign in the alternative hypothesis. A '\\u003e' alternative indicates a right-tailed test, '\\u003c' indicates a left-tailed test, and '≠' indicates a two-tailed test.\"},{\"question\":\"What steps are used to complete a hypothesis test using the P-value or critical value method?\",\"answer\":\"Identify and express the claim symbolically, write H0 and HA, calculate the test statistic, find the P-value or critical value, decide to reject or not reject, and conclude about the claim’s validity.\"}]","Statistics - Hypothesis Testing - Handout | PDF",1791164080,18,{"code":4,"msg":5,"data":32},[33,38,43,46,51,56,60,64,69,72,76],{"id":21,"doc_module":4,"doc_module_name":34,"category_name":35,"show_sort_weight":36,"slug":37},"Document","Story & Novel",90,"story-novel",{"id":39,"doc_module":4,"doc_module_name":34,"category_name":40,"show_sort_weight":41,"slug":42},2,"Literature",80,"literature",{"id":11,"doc_module":4,"doc_module_name":34,"category_name":12,"show_sort_weight":44,"slug":45},70,"exam",{"id":47,"doc_module":4,"doc_module_name":34,"category_name":48,"show_sort_weight":49,"slug":50},5,"Comic",60,"comic",{"id":52,"doc_module":4,"doc_module_name":34,"category_name":53,"show_sort_weight":54,"slug":55},6,"Technology",50,"technology",{"id":22,"doc_module":4,"doc_module_name":34,"category_name":57,"show_sort_weight":58,"slug":59},"Healthcare",40,"healthcare",{"id":20,"doc_module":4,"doc_module_name":34,"category_name":61,"show_sort_weight":62,"slug":63},"Research & Report",30,"research-report",{"id":65,"doc_module":4,"doc_module_name":34,"category_name":66,"show_sort_weight":67,"slug":68},9,"Religion & Spirituality",20,"religion-spirituality",{"id":67,"doc_module":4,"doc_module_name":34,"category_name":70,"show_sort_weight":67,"slug":71},"World Cup","world-cup",{"id":73,"doc_module":4,"doc_module_name":34,"category_name":74,"show_sort_weight":73,"slug":75},10,"Lifestyle","lifestyle",{"id":77,"doc_module":4,"doc_module_name":34,"category_name":78,"show_sort_weight":47,"slug":79},19,"General","general",{"code":4,"msg":81,"data":82},"ok",{"site_id":25,"language":24,"slug":83,"title":13,"keywords":84,"description":14,"schema_data":85,"social_meta":139,"head_meta":141,"extra_data":143,"updated_unix":144},"statistics-hypothesis-testing-handout","",{"@graph":86,"@context":138},[87,101,121],{"@type":88,"itemListElement":89},"BreadcrumbList",[90,94,96,99],{"item":91,"name":92,"@type":93,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":95,"name":34,"@type":93,"position":39},"https://docshare.wps.com/document/",{"item":97,"name":12,"@type":93,"position":98},"https://docshare.wps.com/document/exam/",3,{"item":100,"name":13,"@type":93,"position":11},"https://docshare.wps.com/document/statistics-hypothesis-testing-handout/506379/",{"url":100,"name":13,"@type":102,"image":103,"author":108,"headline":13,"publisher":110,"fileFormat":113,"inLanguage":24,"description":14,"dateModified":114,"datePublished":115,"encodingFormat":113,"isAccessibleForFree":116,"interactionStatistic":117},"DigitalDocument",{"url":104,"@type":105,"width":106,"height":107},"https://docshare.wps.com/thumbnails/statistics-hypothesis-testing-handout/506379.png","ImageObject",300,407,{"name":9,"@type":109},"Person",{"url":91,"name":111,"@type":112},"DocShare","Organization","application/pdf","2026-10-22","2026-10-05",true,{"@type":118,"interactionType":119,"userInteractionCount":20},"InteractionCounter",{"@type":120},"ViewAction",{"@type":122,"mainEntity":123},"FAQPage",[124,130,134],{"name":125,"@type":126,"acceptedAnswer":127},"What is the difference between the null hypothesis and the alternative hypothesis?","Question",{"text":128,"@type":129},"The null hypothesis (H0) is written with equality (e.g., =, ≤, or ≥). The alternative hypothesis (HA, Ha, or H1) is written with an inequality (\u003C, >, or ≠).","Answer",{"name":131,"@type":126,"acceptedAnswer":132},"How do you determine whether a test is right-tailed, left-tailed, or two-tailed?",{"text":133,"@type":129},"Use the inequality sign in the alternative hypothesis. A '>' alternative indicates a right-tailed test, '\u003C' indicates a left-tailed test, and '≠' indicates a two-tailed test.",{"name":135,"@type":126,"acceptedAnswer":136},"What steps are used to complete a hypothesis test using the P-value or critical value method?",{"text":137,"@type":129},"Identify and express the claim symbolically, write H0 and HA, calculate the test statistic, find the P-value or critical value, decide to reject or not reject, and conclude about the claim’s validity.","https://schema.org",{"og:url":100,"og:type":140,"og:title":13,"og:site_name":111,"og:description":14},"article",{"robots":142,"canonical":100},"index,follow",{"doc_id":7,"site_id":25},1791400118]