{"id":5456,"date":"2022-08-30T05:01:15","date_gmt":"2022-08-30T05:01:15","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5456"},"modified":"2022-08-30T05:01:15","modified_gmt":"2022-08-30T05:01:15","slug":"14b-coreq","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/14b-coreq\/","title":{"raw":"14B Coreq","rendered":"14B Coreq"},"content":{"raw":"In the next preview assignment and in the next class, you will need to be able to set up\u00a0 hypothesis tests and use P-values to draw conclusions about population means. You\u00a0 will also need to know how to calculate ratios to determine the test statistic for an\u00a0 ANOVA.\r\n\r\nHypothesis Testing for Means\r\n
\r\n

Question 1<\/h3>\r\n1) We want to test if there is a difference in the mean typing speed (in words per\u00a0 minute) between people who are left-handed and those who are right-handed.\r\n\r\nPart A: How many groups\/populations are we comparing? Name the\u00a0 groups\/populations.\r\n\r\nPart B: Define the parameters of interest in the context of the problem and include\u00a0 the symbols to represent them.\r\n\r\nPart C: What mathematical symbol should the null hypothesis always include? Part D: State the null hypothesis in symbolic form.\r\n\r\nPart E: What question are we trying to answer?\r\n
    \r\n \t
  1. a) Is the mean typing speed for left-handed people different than the mean\u00a0 typing speed for right-handed people?<\/li>\r\n \t
  2. b) Is the mean typing speed for left-handed people greater than the mean typing speed for right-handed people?<\/li>\r\n \t
  3. c) Is the mean typing speed for left-handed people less than the mean typing\u00a0 speed for right-handed people?<\/li>\r\n<\/ol>\r\nPart F: State the alternative hypothesis in symbolic form.\r\n\r\nPart G: If the P-value is less than the level of significance (\ufffd, or alpha), what should\u00a0 you do?\r\n
      \r\n \t
    1. a) Reject the null hypothesis.<\/li>\r\n \t
    2. b) Fail to reject the null hypothesis.<\/li>\r\n \t
    3. c) Accept the null hypothesis.<\/li>\r\n<\/ol>\r\nPart H: If the P-value is greater than the level of significance (\ufffd, or alpha), what\u00a0 should you do?\r\n
        \r\n \t
      1. a) Reject the null hypothesis.<\/li>\r\n \t
      2. b) Fail to reject the null hypothesis.<\/li>\r\n \t
      3. c) Accept the null hypothesis.<\/li>\r\n<\/ol>\r\n<\/div>\r\n
        \r\n

        Question 2<\/h3>\r\n2) Suppose the researcher in Question 1 set the level of significance (\ufffd, or alpha) to\u00a0 0.05. In each of the following scenarios, state whether or not the null hypothesis\u00a0 should be rejected.\r\n\r\nPart A: P-value = 0.4765\r\n\r\nPart B: P-value = 0.0215\r\n\r\n<\/div>\r\n
        \r\n

        Question 3<\/h3>\r\n3) Return to the original scenario in Question 1, and suppose we got a P-value of\u00a0 0.0162.\r\n\r\nPart A: What would be your conclusion in the context of the problem with \ufffd = 0.05?\r\n\r\nPart B: Suppose that the level of significance was changed to 0.01. Using the same\u00a0 P-value as Part A, what would the conclusion be in the context of the\u00a0 problem?\r\n\r\n<\/div>\r\n

        Ratios\u00a0<\/strong><\/p>\r\nIn order to make calculations for an ANOVA, we will need to use ratios.\r\n

        \r\n

        Question 4<\/h3>\r\n4) Label which ratio has the greatest value, which ratio has the least value, and which\u00a0 ratio is closest to 1.\r\n\r\nPart A: #$.&\r\n\r\n#'.$\r\n\r\nPart B: '.()\r\n\r\n#.)\r\n\r\nPart C: )*.#'\r\n\r\n#+.&\r\n\r\n<\/div>\r\n
        \r\n

        Question 5<\/h3>\r\n5) Use the ratio \ufffd = -.to answer the following questions.\r\n\r\nPart A: If \ufffd remains the same, what would you expect to happen to the value of \ufffd if\u00a0 you increase the numerator, \ufffd?\r\n\r\nPart B: If \ufffd remains the same, what would you expect to happen to the value of \ufffd if\u00a0 you increase the denominator, \ufffd?\r\n\r\nPart C: If \ufffd remains the same, what would you expect to happen to the value of \ufffd if\u00a0 you decrease the numerator, \ufffd?\r\n\r\nPart D: If \ufffd remains the same, what would you expect to happen to the value of \ufffd if\u00a0 you decrease the denominator, \ufffd?\r\n\r\n<\/div>","rendered":"

        In the next preview assignment and in the next class, you will need to be able to set up\u00a0 hypothesis tests and use P-values to draw conclusions about population means. You\u00a0 will also need to know how to calculate ratios to determine the test statistic for an\u00a0 ANOVA.<\/p>\n

        Hypothesis Testing for Means<\/p>\n

        \n

        Question 1<\/h3>\n

        1) We want to test if there is a difference in the mean typing speed (in words per\u00a0 minute) between people who are left-handed and those who are right-handed.<\/p>\n

        Part A: How many groups\/populations are we comparing? Name the\u00a0 groups\/populations.<\/p>\n

        Part B: Define the parameters of interest in the context of the problem and include\u00a0 the symbols to represent them.<\/p>\n

        Part C: What mathematical symbol should the null hypothesis always include? Part D: State the null hypothesis in symbolic form.<\/p>\n

        Part E: What question are we trying to answer?<\/p>\n

          \n
        1. a) Is the mean typing speed for left-handed people different than the mean\u00a0 typing speed for right-handed people?<\/li>\n
        2. b) Is the mean typing speed for left-handed people greater than the mean typing speed for right-handed people?<\/li>\n
        3. c) Is the mean typing speed for left-handed people less than the mean typing\u00a0 speed for right-handed people?<\/li>\n<\/ol>\n

          Part F: State the alternative hypothesis in symbolic form.<\/p>\n

          Part G: If the P-value is less than the level of significance (\ufffd, or alpha), what should\u00a0 you do?<\/p>\n

            \n
          1. a) Reject the null hypothesis.<\/li>\n
          2. b) Fail to reject the null hypothesis.<\/li>\n
          3. c) Accept the null hypothesis.<\/li>\n<\/ol>\n

            Part H: If the P-value is greater than the level of significance (\ufffd, or alpha), what\u00a0 should you do?<\/p>\n

              \n
            1. a) Reject the null hypothesis.<\/li>\n
            2. b) Fail to reject the null hypothesis.<\/li>\n
            3. c) Accept the null hypothesis.<\/li>\n<\/ol>\n<\/div>\n
              \n

              Question 2<\/h3>\n

              2) Suppose the researcher in Question 1 set the level of significance (\ufffd, or alpha) to\u00a0 0.05. In each of the following scenarios, state whether or not the null hypothesis\u00a0 should be rejected.<\/p>\n

              Part A: P-value = 0.4765<\/p>\n

              Part B: P-value = 0.0215<\/p>\n<\/div>\n

              \n

              Question 3<\/h3>\n

              3) Return to the original scenario in Question 1, and suppose we got a P-value of\u00a0 0.0162.<\/p>\n

              Part A: What would be your conclusion in the context of the problem with \ufffd = 0.05?<\/p>\n

              Part B: Suppose that the level of significance was changed to 0.01. Using the same\u00a0 P-value as Part A, what would the conclusion be in the context of the\u00a0 problem?<\/p>\n<\/div>\n

              Ratios\u00a0<\/strong><\/p>\n

              In order to make calculations for an ANOVA, we will need to use ratios.<\/p>\n

              \n

              Question 4<\/h3>\n

              4) Label which ratio has the greatest value, which ratio has the least value, and which\u00a0 ratio is closest to 1.<\/p>\n

              Part A: #$.&<\/p>\n

              #’.$<\/p>\n

              Part B: ‘.()<\/p>\n

              #.)<\/p>\n

              Part C: )*.#’<\/p>\n

              #+.&<\/p>\n<\/div>\n

              \n

              Question 5<\/h3>\n

              5) Use the ratio \ufffd = -.to answer the following questions.<\/p>\n

              Part A: If \ufffd remains the same, what would you expect to happen to the value of \ufffd if\u00a0 you increase the numerator, \ufffd?<\/p>\n

              Part B: If \ufffd remains the same, what would you expect to happen to the value of \ufffd if\u00a0 you increase the denominator, \ufffd?<\/p>\n

              Part C: If \ufffd remains the same, what would you expect to happen to the value of \ufffd if\u00a0 you decrease the numerator, \ufffd?<\/p>\n

              Part D: If \ufffd remains the same, what would you expect to happen to the value of \ufffd if\u00a0 you decrease the denominator, \ufffd?<\/p>\n<\/div>\n","protected":false},"author":23592,"menu_order":4,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-5456","chapter","type-chapter","status-publish","hentry"],"part":5448,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5456","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/23592"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5456\/revisions"}],"predecessor-version":[{"id":5457,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5456\/revisions\/5457"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/5448"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5456\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5456"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5456"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5456"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5456"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}