{"id":889,"date":"2021-05-17T13:32:12","date_gmt":"2021-05-17T17:32:12","guid":{"rendered":"https:\/\/openbooks.macewan.ca\/rcommander\/?post_type=part&#038;p=889"},"modified":"2023-12-28T01:31:09","modified_gmt":"2023-12-28T06:31:09","slug":"chapter-8-hypothesis-tests-for-one-population-mean","status":"publish","type":"part","link":"https:\/\/openbooks.macewan.ca\/introstats\/part\/chapter-8-hypothesis-tests-for-one-population-mean\/","title":{"raw":"Chapter 8: Hypothesis Tests for One Population Mean","rendered":"Chapter 8: Hypothesis Tests for One Population Mean"},"content":{"raw":"<h2><strong>Overview<\/strong><\/h2>\r\nRecall that inferential statistics includes estimation and hypothesis testing. Chapter 7 introduces point estimates and confidence intervals (estimation) for the population mean [latex]\\mu[\/latex]. This chapter introduces hypothesis tests for the population mean [latex]\\mu[\/latex].\u00a0Hypothesis tests are used to test statements about the value of the population mean [latex]\\mu[\/latex]. For example:\r\n<ul>\r\n \t<li>A certain brand of energy-saving light bulb advertises that its bulbs last at least 15,000 hours. A contractor suspects this claim is invalid, and he wishes to test if the mean lifespan of bulbs is less than 15,000 hours.<\/li>\r\n \t<li>A factory produces bottles of lotion that are intended to contain 100 ml of lotion. A factory worker performs regular tests to determine if the average volume of bottles differs from 100ml.<\/li>\r\n \t<li>A popular pizzeria wishes to ensure speedy service to customers, so the franchise strives to ensure that its average delivery time is below 30 minutes. After receiving a complaint regarding slow service, the owner decides to conduct a test to see if the average delivery time is above 30 minutes.<\/li>\r\n<\/ul>\r\nHypothesis tests provide a formal tool that can be used to measure the strength of evidence supporting your suspicions.\r\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">Learning Objectives<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nAs a result of completing this chapter, you will be able to do the following:\r\n<ul type=\"disc\">\r\n \t<li>Write down the null and alternative hypotheses for a study.<\/li>\r\n \t<li>Explain the difference between the type I and the type II errors and the relationship between these two types of errors.<\/li>\r\n \t<li>Define the P-value, both mathematically and in plain English.<\/li>\r\n \t<li>Distinguish between the one-mean <em>Z<\/em>\u00a0and the one-mean <i>t-test<\/i>, and identify when each test should be used.<\/li>\r\n \t<li>Conduct a one-mean <em>Z<\/em>\u00a0test and a one-mean <i>t-test<\/i> using the P-value or critical value approaches.<\/li>\r\n \t<li>Calculate the P-value or the range of the P-value for a hypothesis test.<\/li>\r\n \t<li>Explain the relationship between confidence intervals and hypothesis tests.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>","rendered":"<h2><strong>Overview<\/strong><\/h2>\n<p>Recall that inferential statistics includes estimation and hypothesis testing. Chapter 7 introduces point estimates and confidence intervals (estimation) for the population mean [latex]\\mu[\/latex]. This chapter introduces hypothesis tests for the population mean [latex]\\mu[\/latex].\u00a0Hypothesis tests are used to test statements about the value of the population mean [latex]\\mu[\/latex]. For example:<\/p>\n<ul>\n<li>A certain brand of energy-saving light bulb advertises that its bulbs last at least 15,000 hours. A contractor suspects this claim is invalid, and he wishes to test if the mean lifespan of bulbs is less than 15,000 hours.<\/li>\n<li>A factory produces bottles of lotion that are intended to contain 100 ml of lotion. A factory worker performs regular tests to determine if the average volume of bottles differs from 100ml.<\/li>\n<li>A popular pizzeria wishes to ensure speedy service to customers, so the franchise strives to ensure that its average delivery time is below 30 minutes. After receiving a complaint regarding slow service, the owner decides to conduct a test to see if the average delivery time is above 30 minutes.<\/li>\n<\/ul>\n<p>Hypothesis tests provide a formal tool that can be used to measure the strength of evidence supporting your suspicions.<\/p>\n<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">Learning Objectives<\/header>\n<div class=\"textbox__content\">\n<p>As a result of completing this chapter, you will be able to do the following:<\/p>\n<ul type=\"disc\">\n<li>Write down the null and alternative hypotheses for a study.<\/li>\n<li>Explain the difference between the type I and the type II errors and the relationship between these two types of errors.<\/li>\n<li>Define the P-value, both mathematically and in plain English.<\/li>\n<li>Distinguish between the one-mean <em>Z<\/em>\u00a0and the one-mean <i>t-test<\/i>, and identify when each test should be used.<\/li>\n<li>Conduct a one-mean <em>Z<\/em>\u00a0test and a one-mean <i>t-test<\/i> using the P-value or critical value approaches.<\/li>\n<li>Calculate the P-value or the range of the P-value for a hypothesis test.<\/li>\n<li>Explain the relationship between confidence intervals and hypothesis tests.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n","protected":false},"parent":0,"menu_order":8,"template":"","meta":{"pb_part_invisible":false,"pb_part_invisible_string":""},"contributor":[],"license":[],"class_list":["post-889","part","type-part","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts\/889","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts"}],"about":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/types\/part"}],"version-history":[{"count":11,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts\/889\/revisions"}],"predecessor-version":[{"id":4800,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts\/889\/revisions\/4800"}],"wp:attachment":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/media?parent=889"}],"wp:term":[{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/contributor?post=889"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/license?post=889"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}