{"id":5399,"date":"2022-08-20T21:43:37","date_gmt":"2022-08-20T21:43:37","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5399"},"modified":"2022-08-20T22:24:05","modified_gmt":"2022-08-20T22:24:05","slug":"11g-preview","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/11g-preview\/","title":{"raw":"11G Preview","rendered":"11G Preview"},"content":{"raw":"Preparing for the next class\r\n\r\nIn the next in-class activity, you will need to have a firm grasp of how to conduct a two sample test of proportions, including setting up null and alternative hypotheses, checking that necessary conditions have been met, performing the two-sample\u00a0 hypothesis test of proportions, and interpreting the conclusions of the test.\r\n\r\nYou will also need to be able to use the DCMP Compare Two Population Proportions tool at https:\/\/dcmathpathways.shinyapps.io\/2sample_prop\/ to find a confidence interval\u00a0 for the difference between two proportions.\r\n\r\nIn this preview assignment,[footnote]Assignment outline based on lessons from Skew The Script.[\/footnote] you\u2019ll be reading a short article titled \u201cPeople add by default\u00a0 even when subtraction makes more sense\u201d from Science News magazine and\u00a0 analyzing one of the experiments mentioned in the article.\r\n\r\nGo to the article: https:\/\/www.sciencenews.org\/article\/psychology-numbers-people-add default-subtract-better.\r\n\r\nFirst, read the whole article in order to understand the context. Next, focus on the\u00a0 paragraph that describes the experiment involving the Lego structure. There is a picture\u00a0 in the article that illustrates the structure.\r\n\r\nThe following is the paragraph on the Lego structure experiment:\r\n\r\n\u201cIn one experiment, the team offered 197 people wandering around a crowded\u00a0 university quad a dollar to solve a puzzle. Participants viewed a Lego structure in which\u00a0 a figurine was standing atop a platform with a large pillar behind her. Atop that pillar, a\u00a0 single block in one corner supported a flat roof. Researchers asked the participants to\u00a0 stabilize the roof to avoid squashing the figurine. About half the participants were told:\u00a0 \u2018Each piece you add costs 10 cents.\u2019 Even with that financial penalty, only 40 out of 98\u00a0 participants thought to remove the destabilizing block and just rest the roof on top of the\u00a0 wide pillar. The researchers gave the remaining participants a more explicit message:\u00a0 \u2018Each piece you add costs 10 cents but removing pieces is free.\u2019 That cue prompted 60\u00a0 out of 99 participants to remove the block.\u201d\r\n
\r\n

Question 1<\/h3>\r\nLet Group 1 be the group who was told, \u201cEach piece you add costs 10 cents.\u201d Let\u00a0 Group 2 be the group who was told, \u201cEach piece you add costs 10 cents but\u00a0 removing pieces is free.\u201d\r\n
    \r\n \t
  1. Part A: Which of the following is a more appropriate description of the populations\u00a0 under investigation?\r\n
      \r\n \t
    1. a) Population 1 is composed of people who did not get reminded to remove pieces, and Population 2 is composed of people who did get reminded to\u00a0 remove pieces.<\/li>\r\n \t
    2. b) Population 1 is composed of the experiment\u2019s participants who did not get\u00a0 reminded to remove pieces, and Population 2 is composed of the\u00a0 experiment\u2019s participants who did get reminded to remove pieces.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
    3. Part B: Based on the numbers provided in the article (particularly in the paragraph\u00a0 copied at the beginning of the assignment), what do\u00a0[latex]p_{1} [\/latex] and\u00a0[latex]p_{2} [\/latex] represent?\r\n
        \r\n \t
      1. a) The proportion of people in Population 1 and Population 2, respectively, who thought to remove the destabilizing block.<\/li>\r\n \t
      2. b) The proportion of people in Population 1 and Population 2, respectively, who didn\u2019t think to remove the destabilizing block.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
      3. Part C: Which of the following expresses the null hypothesis, [latex] H_{0}[\/latex]?\r\n
          \r\n \t
        1. a) [latex] p_{1} - p_{2} > 0[\/latex]<\/li>\r\n \t
        2. b) [latex] p_{1} - p_{2} < 0[\/latex]<\/li>\r\n \t
        3. c) [latex] p_{1} - p_{2} = 0[\/latex]<\/li>\r\n \t
        4. d) [latex] p_{1} - p_{2} \\neq 0[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
        5. Part D: Suppose that the researchers wanted to test the claim that the proportion of\u00a0 people who remove a piece is different depending on whether people are\u00a0 reminded to remove a piece or not. Which of the following expresses the\u00a0 alternative hypothesis, [latex] H_{A}[\/latex]?\r\n
            \r\n \t
          1. a) [latex] p_{1} - p_{2} > 0[\/latex]<\/li>\r\n \t
          2. b) [latex] p_{1} - p_{2} < 0[\/latex]<\/li>\r\n \t
          3. c) [latex] p_{1} - p_{2} = 0[\/latex]<\/li>\r\n \t
          4. d) [latex] p_{1} - p_{2} \\neq 0[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<\/div>\r\n
            \r\n

            Question 2<\/h3>\r\nNow that we\u2019ve established the null and alternative hypotheses, we need to check\u00a0 that the necessary conditions for conducting a two-sample test of proportions have\u00a0 been met.\r\n
              \r\n \t
            1. Part A: Fill in the following table based on the information in the article.\r\n
              \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
              Symbol<\/td>\r\nMeaning<\/td>\r\nValue<\/td>\r\n<\/tr>\r\n
              [latex] x_{1} [\/latex]<\/td>\r\nNumber of people\u00a0 in Group 1 who\r\n\r\nthought to remove\u00a0 the destabilizing\u00a0 block<\/td>\r\n<\/td>\r\n<\/tr>\r\n
              [latex] n_{1} [\/latex]<\/td>\r\nSize of Group 1<\/td>\r\n<\/td>\r\n<\/tr>\r\n
              [latex] \\hat{p_{1}} [\/latex]<\/td>\r\nProportion of\r\n\r\npeople in Group 1\u00a0 who thought to\r\n\r\nremove the\r\n\r\ndestabilizing block<\/td>\r\n<\/td>\r\n<\/tr>\r\n
              [latex] x_{2} [\/latex]<\/td>\r\nNumber of people\u00a0 in Group 2 who\r\n\r\nthought to remove\u00a0 the destabilizing\u00a0 block<\/td>\r\n<\/td>\r\n<\/tr>\r\n
              [latex] n_{2} [\/latex]<\/td>\r\nSize of Group 2<\/td>\r\n<\/td>\r\n<\/tr>\r\n
              [latex] \\hat{p_{2}} [\/latex]<\/td>\r\nProportion of\r\n\r\npeople in Group 2\u00a0 who thought to\r\n\r\nremove the\r\n\r\ndestabilizing block<\/td>\r\n<\/td>\r\n<\/tr>\r\n
              [latex] \\hat{p_{c}} [\/latex]<\/td>\r\nCombined sample\u00a0 proportion from\r\n\r\nboth groups<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nRecall the necessary conditions for a two-sample test of proportions.\r\n\r\nConditions for Two-Sample Z-Test of Proportions\r\n
                \r\n \t
              1. Large Counts: Check that *MISSING LATEX*<\/li>\r\n<\/ol>\r\n
                  \r\n \t
                1. Random Samples\/Assignment: Check that the two samples<\/li>\r\n<\/ol>\r\nare independent and random samples or that they come from\r\n\r\nrandomly assigned groups in an experiment.\r\n
                    \r\n \t
                  1. 10%: Check that *MISSING LATEX*.<\/li>\r\n<\/ol>\r\n<\/div><\/li>\r\n \t
                  2. \u00a0Part B: Verify Condition 2. Which of the following statements best addresses\u00a0 whether or not this condition was satisfied?\r\n
                      \r\n \t
                    1. a) The article states that study participants were randomly assigned to either\u00a0 Group 1 or Group 2, so this condition was satisfied.<\/li>\r\n \t
                    2. b) The article does not explicitly state that participants were randomly\u00a0 assigned to either Group 1 or Group 2, but we know that the researchers\u00a0 conducted an experiment, so we can safely assume that this condition\u00a0 was satisfied.<\/li>\r\n \t
                    3. c) The article states that the first 98 people were assigned to Group 1 and\u00a0 the next 99 people were assigned to Group 2, so this condition was not\u00a0 satisfied.<\/li>\r\n<\/ol>\r\nPart C: Verify Condition 3. Which of the following best expresses what is true about\u00a0 this condition?\r\n
                        \r\n \t
                      1. a) We only need to check this condition if we are sampling from the population. Since this experiment was done with random assignment, we\u00a0 do not need to check this condition.<\/li>\r\n<\/ol>\r\n \r\n
                          \r\n \t
                        1. b) This condition was met.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
                        2. Part D: Finally, we need to check that we have a large enough sample size to meet Condition 1. Using the table you filled in for Part A of this question, complete the following table.\r\n
                          \r\n\r\n\r\n\r\n\r\n\r\n\r\n
                          [latex] n_{1}\\hat{p_{c}} [\/latex]<\/td>\r\n<\/td>\r\n<\/tr>\r\n
                          [latex] n_{1}(1-\\hat{p_{c}})[\/latex]<\/td>\r\n<\/td>\r\n<\/tr>\r\n
                          [latex] n_{2}\\hat{p_{c}}[\/latex]<\/td>\r\n<\/td>\r\n<\/tr>\r\n
                          [latex] n_{2}(1-\\hat{p_{c}})[\/latex]<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nPart E: Is the sample size large enough to meet the \u201clarge counts\u201d condition?\r\n\r\n<\/div>\r\n
                            \r\n \t
                          1. a) Yes, we found that all values are greater than or equal to 10.<\/li>\r\n \t
                          2. b) No, there are some values that are less than 10.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n \r\n\r\n<\/div>\r\n
                            \r\n

                            Question 3<\/h3>\r\nNow, we are ready to perform the test. We will use significance level \u03b1 = 0.05. Go to\u00a0 the DCMP Compare Two Population Proportions tool at\r\n\r\nhttps:\/\/dcmathpathways.shinyapps.io\/2sample_prop\/.\r\n\r\nUnder \u201cEnter Data,\u201d select \u201cNumber of Successes.\u201d For Group 1 and Group 2, enter\u00a0 the appropriate values and check \u201cProvide Group Labels\u201d to add descriptions for each group.\r\n
                              \r\n \t
                            1. Part A: Under \u201cType of Inference,\u201d select \u201cSignificance Test.\u201d Based on the\u00a0 alternative hypothesis, which option should you select?\r\n
                                \r\n \t
                              1. a) Two-sided<\/li>\r\n \t
                              2. b) Less<\/li>\r\n \t
                              3. c) Greater<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
                              4. Part B: What is the observed difference of sample proportions?<\/li>\r\n \t
                              5. Part C: Select the alternative hypothesis option you chose in Part A. What is the value of the z-test statistic?<\/li>\r\n \t
                              6. Part D: What P-value do you obtain?<\/li>\r\n<\/ol>\r\n<\/div>\r\n
                                \r\n

                                Question 4<\/h3>\r\nIn this question, you will interpret the results of the test using both the z-test statistic\u00a0 and the P-value.\r\n
                                  \r\n \t
                                1. Part A: Which of the following is an appropriate interpretation of the z-test statistic?\r\n
                                    \r\n \t
                                  1. a) Our observed difference of sample proportions (\u2212198) lies 2.78 standard\u00a0 errors below the null hypothesis value. Since this lies more than 2\u00a0 standard errors away, we know this value is quite unlikely, so we have\u00a0 evidence to doubt the null hypothesis.<\/li>\r\n \t
                                  2. b) Our observed difference of sample proportions (\u2212198) lies 2.78 standard\u00a0 errors above the null hypothesis value. Since this lies more than 2\u00a0 standard errors away, we know this value is very likely, so we don\u2019t have\u00a0 evidence to doubt the null hypothesis.<\/li>\r\n \t
                                  3. c) If we assume the null is true, there is a probability of 2.78 of seeing a\u00a0 sample difference of proportions of \u2212198 or more by chance alone. This\u00a0 is very unlikely under the null, so we have reason to doubt the null\u00a0 hypothesis.<\/li>\r\n \t
                                  4. d) There is a probability of 2.78 that the null hypothesis is true.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
                                  5. Part B: Which of the following is an appropriate interpretation of the P-value?\r\n
                                      \r\n \t
                                    1. a) Our observed difference of sample proportions (\u20130.198) lies 0.0055 standard errors below the null hypothesis value. Since this lies less than 2\u00a0 standard errors away, we know this value is quite unlikely, so we have\u00a0 evidence to doubt the null hypothesis.<\/li>\r\n \t
                                    2. b) Our observed difference of sample proportions (\u2212198) lies 0.0055 standard errors above the null hypothesis value. Since this lies less than 2\u00a0 standard errors away, we know this value is very likely, so we don\u2019t have\u00a0 evidence to doubt the null hypothesis.<\/li>\r\n \t
                                    3. c) If we assume the null is true, there is a probability of 0.0055 of seeing a\u00a0 sample difference of proportions of \u2212198 or more by chance alone. This\u00a0 is very unlikely under the null, so we have reason to doubt the null\u00a0 hypothesis.<\/li>\r\n \t
                                    4. d) There is a probability of 0.0055 that the null hypothesis is true.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
                                    5. Part C: Fill in the blank to express your conclusion.\r\nUnder my assumption that there is no difference in proportions of people\u00a0 who chose to remove Lego pieces, the observed data (a difference of\u00a0 \u22120.198 between the two groups among 197 participants) is highly unlikely.\r\nTherefore, I _______ the assumption that there is no difference between the\u00a0 two groups. There is evidence that the proportion of people who remove a\u00a0 piece is different depending on whether people are reminded to remove a\u00a0 piece or not.\r\n
                                        \r\n \t
                                      1. a) reject<\/li>\r\n \t
                                      2. b) fail to reject<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<\/div>\r\nLooking Ahead\r\n
                                        \r\n

                                        Question 5<\/h3>\r\nIn the next class, you will need to be able to use the data analysis tool to find a\u00a0 confidence interval for the difference between two proportions. To do this, under\u00a0 \u201cType of Inference,\u201d select \u201cConfidence Interval.\u201d Construct a 95% confidence\u00a0 interval.\r\n
                                          \r\n \t
                                        1. Part A: What are the lower and upper bounds of the confidence interval you obtain\u00a0 for [latex] p_{1} - p_{2} [\/latex]? Fill in the following table and round to 3 decimal places.\r\n
                                          \r\n\r\n\r\n\r\n\r\n
                                          Lower bound<\/td>\r\n<\/td>\r\n<\/tr>\r\n
                                          Upper bound<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div><\/li>\r\n \t
                                        2. Part B: Determine whether this statement is true or false: \u201cThere is a 95% chance\u00a0 that the true difference in population proportions lies between \u22120.335 and\u00a0 \u22120.061.\u201d\r\n
                                            \r\n \t
                                          1. a) True<\/li>\r\n \t
                                          2. b) False<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<\/div>","rendered":"

                                            Preparing for the next class<\/p>\n

                                            In the next in-class activity, you will need to have a firm grasp of how to conduct a two sample test of proportions, including setting up null and alternative hypotheses, checking that necessary conditions have been met, performing the two-sample\u00a0 hypothesis test of proportions, and interpreting the conclusions of the test.<\/p>\n

                                            You will also need to be able to use the DCMP Compare Two Population Proportions tool at https:\/\/dcmathpathways.shinyapps.io\/2sample_prop\/ to find a confidence interval\u00a0 for the difference between two proportions.<\/p>\n

                                            In this preview assignment,[1]<\/sup><\/a> you\u2019ll be reading a short article titled \u201cPeople add by default\u00a0 even when subtraction makes more sense\u201d from Science News magazine and\u00a0 analyzing one of the experiments mentioned in the article.<\/p>\n

                                            Go to the article: https:\/\/www.sciencenews.org\/article\/psychology-numbers-people-add default-subtract-better.<\/p>\n

                                            First, read the whole article in order to understand the context. Next, focus on the\u00a0 paragraph that describes the experiment involving the Lego structure. There is a picture\u00a0 in the article that illustrates the structure.<\/p>\n

                                            The following is the paragraph on the Lego structure experiment:<\/p>\n

                                            \u201cIn one experiment, the team offered 197 people wandering around a crowded\u00a0 university quad a dollar to solve a puzzle. Participants viewed a Lego structure in which\u00a0 a figurine was standing atop a platform with a large pillar behind her. Atop that pillar, a\u00a0 single block in one corner supported a flat roof. Researchers asked the participants to\u00a0 stabilize the roof to avoid squashing the figurine. About half the participants were told:\u00a0 \u2018Each piece you add costs 10 cents.\u2019 Even with that financial penalty, only 40 out of 98\u00a0 participants thought to remove the destabilizing block and just rest the roof on top of the\u00a0 wide pillar. The researchers gave the remaining participants a more explicit message:\u00a0 \u2018Each piece you add costs 10 cents but removing pieces is free.\u2019 That cue prompted 60\u00a0 out of 99 participants to remove the block.\u201d<\/p>\n

                                            \n

                                            Question 1<\/h3>\n

                                            Let Group 1 be the group who was told, \u201cEach piece you add costs 10 cents.\u201d Let\u00a0 Group 2 be the group who was told, \u201cEach piece you add costs 10 cents but\u00a0 removing pieces is free.\u201d<\/p>\n

                                              \n
                                            1. Part A: Which of the following is a more appropriate description of the populations\u00a0 under investigation?\n
                                                \n
                                              1. a) Population 1 is composed of people who did not get reminded to remove pieces, and Population 2 is composed of people who did get reminded to\u00a0 remove pieces.<\/li>\n
                                              2. b) Population 1 is composed of the experiment\u2019s participants who did not get\u00a0 reminded to remove pieces, and Population 2 is composed of the\u00a0 experiment\u2019s participants who did get reminded to remove pieces.<\/li>\n<\/ol>\n<\/li>\n
                                              3. Part B: Based on the numbers provided in the article (particularly in the paragraph\u00a0 copied at the beginning of the assignment), what do\u00a0[latex]p_{1}[\/latex] and\u00a0[latex]p_{2}[\/latex] represent?\n
                                                  \n
                                                1. a) The proportion of people in Population 1 and Population 2, respectively, who thought to remove the destabilizing block.<\/li>\n
                                                2. b) The proportion of people in Population 1 and Population 2, respectively, who didn\u2019t think to remove the destabilizing block.<\/li>\n<\/ol>\n<\/li>\n
                                                3. Part C: Which of the following expresses the null hypothesis, [latex]H_{0}[\/latex]?\n
                                                    \n
                                                  1. a) [latex]p_{1} - p_{2} > 0[\/latex]<\/li>\n
                                                  2. b) [latex]p_{1} - p_{2} < 0[\/latex]<\/li>\n
                                                  3. c) [latex]p_{1} - p_{2} = 0[\/latex]<\/li>\n
                                                  4. d) [latex]p_{1} - p_{2} \\neq 0[\/latex]<\/li>\n<\/ol>\n<\/li>\n
                                                  5. Part D: Suppose that the researchers wanted to test the claim that the proportion of\u00a0 people who remove a piece is different depending on whether people are\u00a0 reminded to remove a piece or not. Which of the following expresses the\u00a0 alternative hypothesis, [latex]H_{A}[\/latex]?\n
                                                      \n
                                                    1. a) [latex]p_{1} - p_{2} > 0[\/latex]<\/li>\n
                                                    2. b) [latex]p_{1} - p_{2} < 0[\/latex]<\/li>\n
                                                    3. c) [latex]p_{1} - p_{2} = 0[\/latex]<\/li>\n
                                                    4. d) [latex]p_{1} - p_{2} \\neq 0[\/latex]<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/div>\n
                                                      \n

                                                      Question 2<\/h3>\n

                                                      Now that we\u2019ve established the null and alternative hypotheses, we need to check\u00a0 that the necessary conditions for conducting a two-sample test of proportions have\u00a0 been met.<\/p>\n

                                                        \n
                                                      1. Part A: Fill in the following table based on the information in the article.\n
                                                        \n\n\n\n\n\n\n\n\n\n\n
                                                        Symbol<\/td>\nMeaning<\/td>\nValue<\/td>\n<\/tr>\n
                                                        [latex]x_{1}[\/latex]<\/td>\nNumber of people\u00a0 in Group 1 who<\/p>\n

                                                        thought to remove\u00a0 the destabilizing\u00a0 block<\/td>\n

                                                        		<\/td>\n<\/tr>\n
                                                        [latex]n_{1}[\/latex]<\/td>\nSize of Group 1<\/td>\n<\/td>\n<\/tr>\n
                                                        [latex]\\hat{p_{1}}[\/latex]<\/td>\nProportion of<\/p>\n

                                                        people in Group 1\u00a0 who thought to<\/p>\n

                                                        remove the<\/p>\n

                                                        destabilizing block<\/td>\n

                                                        		<\/td>\n<\/tr>\n
                                                        [latex]x_{2}[\/latex]<\/td>\nNumber of people\u00a0 in Group 2 who<\/p>\n

                                                        thought to remove\u00a0 the destabilizing\u00a0 block<\/td>\n

                                                        		<\/td>\n<\/tr>\n
                                                        [latex]n_{2}[\/latex]<\/td>\nSize of Group 2<\/td>\n<\/td>\n<\/tr>\n
                                                        [latex]\\hat{p_{2}}[\/latex]<\/td>\nProportion of<\/p>\n

                                                        people in Group 2\u00a0 who thought to<\/p>\n

                                                        remove the<\/p>\n

                                                        destabilizing block<\/td>\n

                                                        		<\/td>\n<\/tr>\n
                                                        [latex]\\hat{p_{c}}[\/latex]<\/td>\nCombined sample\u00a0 proportion from<\/p>\n

                                                        both groups<\/td>\n

                                                        		<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                                                        Recall the necessary conditions for a two-sample test of proportions.<\/p>\n

                                                        Conditions for Two-Sample Z-Test of Proportions<\/p>\n

                                                          \n
                                                        1. Large Counts: Check that *MISSING LATEX*<\/li>\n<\/ol>\n
                                                            \n
                                                          1. Random Samples\/Assignment: Check that the two samples<\/li>\n<\/ol>\n

                                                            are independent and random samples or that they come from<\/p>\n

                                                            randomly assigned groups in an experiment.<\/p>\n

                                                              \n
                                                            1. 10%: Check that *MISSING LATEX*.<\/li>\n<\/ol>\n<\/div>\n<\/li>\n
                                                            2. \u00a0Part B: Verify Condition 2. Which of the following statements best addresses\u00a0 whether or not this condition was satisfied?\n
                                                                \n
                                                              1. a) The article states that study participants were randomly assigned to either\u00a0 Group 1 or Group 2, so this condition was satisfied.<\/li>\n
                                                              2. b) The article does not explicitly state that participants were randomly\u00a0 assigned to either Group 1 or Group 2, but we know that the researchers\u00a0 conducted an experiment, so we can safely assume that this condition\u00a0 was satisfied.<\/li>\n
                                                              3. c) The article states that the first 98 people were assigned to Group 1 and\u00a0 the next 99 people were assigned to Group 2, so this condition was not\u00a0 satisfied.<\/li>\n<\/ol>\n

                                                                Part C: Verify Condition 3. Which of the following best expresses what is true about\u00a0 this condition?<\/p>\n

                                                                  \n
                                                                1. a) We only need to check this condition if we are sampling from the population. Since this experiment was done with random assignment, we\u00a0 do not need to check this condition.<\/li>\n<\/ol>\n

                                                                   <\/p>\n

                                                                    \n
                                                                  1. b) This condition was met.<\/li>\n<\/ol>\n<\/li>\n
                                                                  2. Part D: Finally, we need to check that we have a large enough sample size to meet Condition 1. Using the table you filled in for Part A of this question, complete the following table.\n
                                                                    \n\n\n\n\n\n\n
                                                                    [latex]n_{1}\\hat{p_{c}}[\/latex]<\/td>\n<\/td>\n<\/tr>\n
                                                                    [latex]n_{1}(1-\\hat{p_{c}})[\/latex]<\/td>\n<\/td>\n<\/tr>\n
                                                                    [latex]n_{2}\\hat{p_{c}}[\/latex]<\/td>\n<\/td>\n<\/tr>\n
                                                                    [latex]n_{2}(1-\\hat{p_{c}})[\/latex]<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                                                                    Part E: Is the sample size large enough to meet the \u201clarge counts\u201d condition?<\/p>\n<\/div>\n

                                                                      \n
                                                                    1. a) Yes, we found that all values are greater than or equal to 10.<\/li>\n
                                                                    2. b) No, there are some values that are less than 10.<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                                                                       <\/p>\n<\/div>\n

                                                                      \n

                                                                      Question 3<\/h3>\n

                                                                      Now, we are ready to perform the test. We will use significance level \u03b1 = 0.05. Go to\u00a0 the DCMP Compare Two Population Proportions tool at<\/p>\n

                                                                      https:\/\/dcmathpathways.shinyapps.io\/2sample_prop\/.<\/p>\n

                                                                      Under \u201cEnter Data,\u201d select \u201cNumber of Successes.\u201d For Group 1 and Group 2, enter\u00a0 the appropriate values and check \u201cProvide Group Labels\u201d to add descriptions for each group.<\/p>\n

                                                                        \n
                                                                      1. Part A: Under \u201cType of Inference,\u201d select \u201cSignificance Test.\u201d Based on the\u00a0 alternative hypothesis, which option should you select?\n
                                                                          \n
                                                                        1. a) Two-sided<\/li>\n
                                                                        2. b) Less<\/li>\n
                                                                        3. c) Greater<\/li>\n<\/ol>\n<\/li>\n
                                                                        4. Part B: What is the observed difference of sample proportions?<\/li>\n
                                                                        5. Part C: Select the alternative hypothesis option you chose in Part A. What is the value of the z-test statistic?<\/li>\n
                                                                        6. Part D: What P-value do you obtain?<\/li>\n<\/ol>\n<\/div>\n
                                                                          \n

                                                                          Question 4<\/h3>\n

                                                                          In this question, you will interpret the results of the test using both the z-test statistic\u00a0 and the P-value.<\/p>\n

                                                                            \n
                                                                          1. Part A: Which of the following is an appropriate interpretation of the z-test statistic?\n
                                                                              \n
                                                                            1. a) Our observed difference of sample proportions (\u2212198) lies 2.78 standard\u00a0 errors below the null hypothesis value. Since this lies more than 2\u00a0 standard errors away, we know this value is quite unlikely, so we have\u00a0 evidence to doubt the null hypothesis.<\/li>\n
                                                                            2. b) Our observed difference of sample proportions (\u2212198) lies 2.78 standard\u00a0 errors above the null hypothesis value. Since this lies more than 2\u00a0 standard errors away, we know this value is very likely, so we don\u2019t have\u00a0 evidence to doubt the null hypothesis.<\/li>\n
                                                                            3. c) If we assume the null is true, there is a probability of 2.78 of seeing a\u00a0 sample difference of proportions of \u2212198 or more by chance alone. This\u00a0 is very unlikely under the null, so we have reason to doubt the null\u00a0 hypothesis.<\/li>\n
                                                                            4. d) There is a probability of 2.78 that the null hypothesis is true.<\/li>\n<\/ol>\n<\/li>\n
                                                                            5. Part B: Which of the following is an appropriate interpretation of the P-value?\n
                                                                                \n
                                                                              1. a) Our observed difference of sample proportions (\u20130.198) lies 0.0055 standard errors below the null hypothesis value. Since this lies less than 2\u00a0 standard errors away, we know this value is quite unlikely, so we have\u00a0 evidence to doubt the null hypothesis.<\/li>\n
                                                                              2. b) Our observed difference of sample proportions (\u2212198) lies 0.0055 standard errors above the null hypothesis value. Since this lies less than 2\u00a0 standard errors away, we know this value is very likely, so we don\u2019t have\u00a0 evidence to doubt the null hypothesis.<\/li>\n
                                                                              3. c) If we assume the null is true, there is a probability of 0.0055 of seeing a\u00a0 sample difference of proportions of \u2212198 or more by chance alone. This\u00a0 is very unlikely under the null, so we have reason to doubt the null\u00a0 hypothesis.<\/li>\n
                                                                              4. d) There is a probability of 0.0055 that the null hypothesis is true.<\/li>\n<\/ol>\n<\/li>\n
                                                                              5. Part C: Fill in the blank to express your conclusion.
                                                                                \nUnder my assumption that there is no difference in proportions of people\u00a0 who chose to remove Lego pieces, the observed data (a difference of\u00a0 \u22120.198 between the two groups among 197 participants) is highly unlikely.
                                                                                \nTherefore, I _______ the assumption that there is no difference between the\u00a0 two groups. There is evidence that the proportion of people who remove a\u00a0 piece is different depending on whether people are reminded to remove a\u00a0 piece or not.<\/p>\n
                                                                                  \n
                                                                                1. a) reject<\/li>\n
                                                                                2. b) fail to reject<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/div>\n

                                                                                  Looking Ahead<\/p>\n

                                                                                  \n

                                                                                  Question 5<\/h3>\n

                                                                                  In the next class, you will need to be able to use the data analysis tool to find a\u00a0 confidence interval for the difference between two proportions. To do this, under\u00a0 \u201cType of Inference,\u201d select \u201cConfidence Interval.\u201d Construct a 95% confidence\u00a0 interval.<\/p>\n

                                                                                    \n
                                                                                  1. Part A: What are the lower and upper bounds of the confidence interval you obtain\u00a0 for [latex]p_{1} - p_{2}[\/latex]? Fill in the following table and round to 3 decimal places.\n
                                                                                    \n\n\n\n\n
                                                                                    Lower bound<\/td>\n<\/td>\n<\/tr>\n
                                                                                    Upper bound<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/li>\n
                                                                                  2. Part B: Determine whether this statement is true or false: \u201cThere is a 95% chance\u00a0 that the true difference in population proportions lies between \u22120.335 and\u00a0 \u22120.061.\u201d\n
                                                                                      \n
                                                                                    1. a) True<\/li>\n
                                                                                    2. b) False<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/div>\n
                                                                                      1. Assignment outline based on lessons from Skew The Script. ↵<\/a><\/li><\/ol><\/div>","protected":false},"author":574340,"menu_order":21,"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-5399","chapter","type-chapter","status-publish","hentry"],"part":5305,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5399","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\/574340"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5399\/revisions"}],"predecessor-version":[{"id":5413,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5399\/revisions\/5413"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/5305"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5399\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5399"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5399"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5399"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5399"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}