{"id":4937,"date":"2022-08-16T22:44:34","date_gmt":"2022-08-16T22:44:34","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=4937"},"modified":"2022-08-23T05:56:12","modified_gmt":"2022-08-23T05:56:12","slug":"13c-coreq","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/13c-coreq\/","title":{"raw":"13C Coreq","rendered":"13C Coreq"},"content":{"raw":"In the next preview assignment and in the next class, you will need to be able to rewrite\u00a0 equations and inequalities, use formulas to make inferences about two means, and\u00a0 calculate a difference between two measurements.\r\n

Screen Time Across America\u00a0<\/strong><\/p>\r\nIn 2018, Apple released a program that tracks screen time usage on their phones. In\u00a0 order to have a good idea of how much time Americans spend on their phones, a study\u00a0 was conducted with 2,103 participants. The dataset we are going to look at for this\u00a0 corequisite support activity contains the mean daily data usage for Apple users in each\u00a0 of the 50 states across America.[footnote]Wilkinson, D. (n.d.). Screen time trends in the age of COVID-19. SimpleTexting.\u00a0 https:\/\/simpletexting.com\/screentime-smartphone-usage-statistics\/[\/footnote] To read more about this study, go to https:\/\/simpletexting.com\/screen-time-survey\/.\r\n\r\nGo to the DCMP Describing and Exploring Quantitative Variables tool at\u00a0 https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/.\r\n\r\nNext, locate \u201cEnter Data\u201d on the drop-down menu and select \u201cYour Own.\u201d For \u201cName of Variable,\u201d type in \u201cAverage Daily Screen Time (in minutes)\u201d and then copy and paste\u00a0 the following daily screen time data (continued on the following page) in the \u201cEnter\u00a0 Observations\u201d box.\r\n

\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
State<\/strong><\/td>\r\nAverage Daily\u00a0 Screen Time\u00a0\u00a0<\/strong>\r\n\r\n(in minutes)<\/strong><\/td>\r\n<\/td>\r\nState<\/strong><\/td>\r\nAverage Daily\u00a0 Screen Time\u00a0 (in minutes)<\/strong><\/td>\r\n<\/tr>\r\n
Alabama<\/td>\r\n170<\/td>\r\n<\/td>\r\nMontana<\/td>\r\n154<\/td>\r\n<\/tr>\r\n
Alaska<\/td>\r\n134<\/td>\r\n<\/td>\r\nNebraska<\/td>\r\n182<\/td>\r\n<\/tr>\r\n
Arizona<\/td>\r\n276<\/td>\r\n<\/td>\r\nNevada<\/td>\r\n262<\/td>\r\n<\/tr>\r\n
Arkansas<\/td>\r\n145<\/td>\r\n<\/td>\r\nNew Hampshire<\/td>\r\n135<\/td>\r\n<\/tr>\r\n
California<\/td>\r\n204<\/td>\r\n<\/td>\r\nNew Jersey<\/td>\r\n182<\/td>\r\n<\/tr>\r\n
Colorado<\/td>\r\n166<\/td>\r\n<\/td>\r\nNew Mexico<\/td>\r\n177<\/td>\r\n<\/tr>\r\n
Connecticut<\/td>\r\n262<\/td>\r\n<\/td>\r\nNew York<\/td>\r\n206<\/td>\r\n<\/tr>\r\n
Delaware<\/td>\r\n166<\/td>\r\n<\/td>\r\nNorth Carolina<\/td>\r\n205<\/td>\r\n<\/tr>\r\n
Florida<\/td>\r\n213<\/td>\r\n<\/td>\r\nNorth Dakota<\/td>\r\n192<\/td>\r\n<\/tr>\r\n
Georgia<\/td>\r\n198<\/td>\r\n<\/td>\r\nOhio<\/td>\r\n231<\/td>\r\n<\/tr>\r\n
Hawaii<\/td>\r\n133<\/td>\r\n<\/td>\r\nOklahoma<\/td>\r\n131<\/td>\r\n<\/tr>\r\n
Idaho<\/td>\r\n161<\/td>\r\n<\/td>\r\nOregon<\/td>\r\n132<\/td>\r\n<\/tr>\r\n
Illinois<\/td>\r\n220<\/td>\r\n<\/td>\r\nPennsylvania<\/td>\r\n213<\/td>\r\n<\/tr>\r\n
Indiana<\/td>\r\n220<\/td>\r\n<\/td>\r\nRhode Island<\/td>\r\n165<\/td>\r\n<\/tr>\r\n
Iowa<\/td>\r\n163<\/td>\r\n<\/td>\r\nSouth Carolina<\/td>\r\n155<\/td>\r\n<\/tr>\r\n
Kansas<\/td>\r\n146<\/td>\r\n<\/td>\r\nSouth Dakota<\/td>\r\n154<\/td>\r\n<\/tr>\r\n
Kentucky<\/td>\r\n149<\/td>\r\n<\/td>\r\nTennessee<\/td>\r\n196<\/td>\r\n<\/tr>\r\n
Louisiana<\/td>\r\n144<\/td>\r\n<\/td>\r\nTexas<\/td>\r\n186<\/td>\r\n<\/tr>\r\n
Maine<\/td>\r\n165<\/td>\r\n<\/td>\r\nUtah<\/td>\r\n155<\/td>\r\n<\/tr>\r\n
Maryland<\/td>\r\n199<\/td>\r\n<\/td>\r\nVermont<\/td>\r\n124<\/td>\r\n<\/tr>\r\n
Massachusetts<\/td>\r\n195<\/td>\r\n<\/td>\r\nVirginia<\/td>\r\n179<\/td>\r\n<\/tr>\r\n
Michigan<\/td>\r\n188<\/td>\r\n<\/td>\r\nWashington<\/td>\r\n173<\/td>\r\n<\/tr>\r\n
Minnesota<\/td>\r\n140<\/td>\r\n<\/td>\r\nWest Virginia<\/td>\r\n150<\/td>\r\n<\/tr>\r\n
Mississippi<\/td>\r\n146<\/td>\r\n<\/td>\r\nWisconsin<\/td>\r\n211<\/td>\r\n<\/tr>\r\n
Missouri<\/td>\r\n211<\/td>\r\n<\/td>\r\nWyoming<\/td>\r\n134<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n
\r\n

Question 1<\/h3>\r\n1) What is the mean you calculated using the data analysis tool?\r\n\r\n<\/div>\r\n
\r\n

Question 2<\/h3>\r\n2) What does the mean represent in this context?\r\n\r\n<\/div>\r\n
\r\n

Question 3<\/h3>\r\n3) We are going to see how far above and below the mean the average daily screen\u00a0 time (in minutes) is for some states. In order to find this difference, use the following\u00a0 formula:\r\n\r\nDifference = (average daily screen time, in minutes) \u2013 (mean)\r\n\r\nFor example, for Alabama, we would take the average daily screen time (170) and\u00a0 subtract the mean (178): 170 \u2013 178 = \u20138\r\n\r\na) Find the difference between Oregon and the mean.\r\n\r\nb) Describe what this difference represents in this context.\r\n\r\nc) Find the difference between Michigan and the mean.\r\n\r\nd) Describe what this difference represents in this context.\r\n\r\n<\/div>\r\n
\r\n

Question 4<\/h3>\r\n4) If you live in a different state than the two above, find the difference between the\u00a0 state you live in and the mean. Describe what the difference represents in this\u00a0 context.\r\n\r\n<\/div>\r\n
\r\n

Question 5<\/h3>\r\n5) Consider the equation [latex]a=b[\/latex]. You can rewrite this equation in an equivalent form that has 0 on the right side by subtracting [latex]b[\/latex] from both sides, as follows:\r\n\r\n[latex]a=b[\/latex]\r\n\r\n[latex]a-b=b-b[\/latex]\r\n\r\n[latex]a-b=0[\/latex]\r\n\r\na) Consider the equation [latex]\\mu_{1}=\\mu_{2}[\/latex]. Rewrite this equation in an equivalent form that has 0 on the right side by subtracting [latex]\\mu_{2}[\/latex] from both sides.\r\n\r\nb) Consider the inequality [latex]\\mu_{1}<\\mu_{2}[\/latex]. Rewrite this inequality in an equivalent form that has 0 on the right side by subtracting [latex]\\mu_{2}[\/latex] from both sides.\r\n\r\nc) Consider the inequality [latex]\\mu_{1}>\\mu_{2}[\/latex]. Rewrite this inequality in an equivalent form that has 0 on the right side by subtracting\u00a0[latex]\\mu_{2}[\/latex] from both sides.\r\n\r\n<\/div>\r\n
\r\n

Question 6<\/h3>\r\n6) Provide plausible values for the population mean that would make the following statements true.<\/span>\r\n\r\na) [latex]\\mu_{1}-\\mu_{2}=0[\/latex]\r\n\r\nb) [latex]\\mu_{1}-\\mu_{2}<0[\/latex]\r\n\r\nc) [latex]\\mu_{1}-\\mu_{2}>0[\/latex]\r\n\r\n<\/div>\r\n
\r\n

Question 7<\/h3>\r\n7) The formula for the test statistic to compare two population means contains multiple\u00a0 values for the sample mean, sample standard deviation, sample size, and population\u00a0 mean. To prepare for the preview assignment and in-class activity, match each symbol in the following table with its description by drawing lines between them.\r\n
\r\n\r\n\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\n<\/td>\r\nDescription<\/td>\r\n<\/tr>\r\n
[latex]s_{1}[\/latex]<\/td>\r\n<\/td>\r\ndifference between the population means<\/td>\r\n<\/tr>\r\n
[latex]n_{1}[\/latex]<\/td>\r\n<\/td>\r\npopulation mean of Group 1<\/td>\r\n<\/tr>\r\n
[latex]\\bar{x}_{2}[\/latex]<\/td>\r\n<\/td>\r\nsample standard deviation of Group 1<\/td>\r\n<\/tr>\r\n
[latex]\\mu_{2}[\/latex]<\/td>\r\n<\/td>\r\nsample size of Group 1<\/td>\r\n<\/tr>\r\n
[latex]\\mu_{1}-\\mu_{2}[\/latex]<\/td>\r\n<\/td>\r\nsample mean of Group 2<\/td>\r\n<\/tr>\r\n
[latex]s_{2}[\/latex]<\/td>\r\n<\/td>\r\ndifference between the sample means<\/td>\r\n<\/tr>\r\n
[latex]n_{2}[\/latex]<\/td>\r\n<\/td>\r\nsample mean of Group 1<\/td>\r\n<\/tr>\r\n
[latex]\\mu_{1}[\/latex]<\/td>\r\n<\/td>\r\npopulation mean of Group 2<\/td>\r\n<\/tr>\r\n
[latex]\\bar{x}_{1}-\\bar{x}_{2}[\/latex]<\/td>\r\n<\/td>\r\nsample size of Group 2<\/td>\r\n<\/tr>\r\n
[latex]\\bar{x}_{1}[\/latex]<\/td>\r\n<\/td>\r\nsample standard deviation of Group 2<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>","rendered":"

In the next preview assignment and in the next class, you will need to be able to rewrite\u00a0 equations and inequalities, use formulas to make inferences about two means, and\u00a0 calculate a difference between two measurements.<\/p>\n

Screen Time Across America\u00a0<\/strong><\/p>\n

In 2018, Apple released a program that tracks screen time usage on their phones. In\u00a0 order to have a good idea of how much time Americans spend on their phones, a study\u00a0 was conducted with 2,103 participants. The dataset we are going to look at for this\u00a0 corequisite support activity contains the mean daily data usage for Apple users in each\u00a0 of the 50 states across America.[1]<\/sup><\/a> To read more about this study, go to https:\/\/simpletexting.com\/screen-time-survey\/.<\/p>\n

Go to the DCMP Describing and Exploring Quantitative Variables tool at\u00a0 https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/.<\/p>\n

Next, locate \u201cEnter Data\u201d on the drop-down menu and select \u201cYour Own.\u201d For \u201cName of Variable,\u201d type in \u201cAverage Daily Screen Time (in minutes)\u201d and then copy and paste\u00a0 the following daily screen time data (continued on the following page) in the \u201cEnter\u00a0 Observations\u201d box.<\/p>\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
State<\/strong><\/td>\nAverage Daily\u00a0 Screen Time\u00a0\u00a0<\/strong><\/p>\n

(in minutes)<\/strong><\/td>\n

<\/td>\nState<\/strong><\/td>\nAverage Daily\u00a0 Screen Time\u00a0 (in minutes)<\/strong><\/td>\n<\/tr>\n
Alabama<\/td>\n170<\/td>\n<\/td>\nMontana<\/td>\n154<\/td>\n<\/tr>\n
Alaska<\/td>\n134<\/td>\n<\/td>\nNebraska<\/td>\n182<\/td>\n<\/tr>\n
Arizona<\/td>\n276<\/td>\n<\/td>\nNevada<\/td>\n262<\/td>\n<\/tr>\n
Arkansas<\/td>\n145<\/td>\n<\/td>\nNew Hampshire<\/td>\n135<\/td>\n<\/tr>\n
California<\/td>\n204<\/td>\n<\/td>\nNew Jersey<\/td>\n182<\/td>\n<\/tr>\n
Colorado<\/td>\n166<\/td>\n<\/td>\nNew Mexico<\/td>\n177<\/td>\n<\/tr>\n
Connecticut<\/td>\n262<\/td>\n<\/td>\nNew York<\/td>\n206<\/td>\n<\/tr>\n
Delaware<\/td>\n166<\/td>\n<\/td>\nNorth Carolina<\/td>\n205<\/td>\n<\/tr>\n
Florida<\/td>\n213<\/td>\n<\/td>\nNorth Dakota<\/td>\n192<\/td>\n<\/tr>\n
Georgia<\/td>\n198<\/td>\n<\/td>\nOhio<\/td>\n231<\/td>\n<\/tr>\n
Hawaii<\/td>\n133<\/td>\n<\/td>\nOklahoma<\/td>\n131<\/td>\n<\/tr>\n
Idaho<\/td>\n161<\/td>\n<\/td>\nOregon<\/td>\n132<\/td>\n<\/tr>\n
Illinois<\/td>\n220<\/td>\n<\/td>\nPennsylvania<\/td>\n213<\/td>\n<\/tr>\n
Indiana<\/td>\n220<\/td>\n<\/td>\nRhode Island<\/td>\n165<\/td>\n<\/tr>\n
Iowa<\/td>\n163<\/td>\n<\/td>\nSouth Carolina<\/td>\n155<\/td>\n<\/tr>\n
Kansas<\/td>\n146<\/td>\n<\/td>\nSouth Dakota<\/td>\n154<\/td>\n<\/tr>\n
Kentucky<\/td>\n149<\/td>\n<\/td>\nTennessee<\/td>\n196<\/td>\n<\/tr>\n
Louisiana<\/td>\n144<\/td>\n<\/td>\nTexas<\/td>\n186<\/td>\n<\/tr>\n
Maine<\/td>\n165<\/td>\n<\/td>\nUtah<\/td>\n155<\/td>\n<\/tr>\n
Maryland<\/td>\n199<\/td>\n<\/td>\nVermont<\/td>\n124<\/td>\n<\/tr>\n
Massachusetts<\/td>\n195<\/td>\n<\/td>\nVirginia<\/td>\n179<\/td>\n<\/tr>\n
Michigan<\/td>\n188<\/td>\n<\/td>\nWashington<\/td>\n173<\/td>\n<\/tr>\n
Minnesota<\/td>\n140<\/td>\n<\/td>\nWest Virginia<\/td>\n150<\/td>\n<\/tr>\n
Mississippi<\/td>\n146<\/td>\n<\/td>\nWisconsin<\/td>\n211<\/td>\n<\/tr>\n
Missouri<\/td>\n211<\/td>\n<\/td>\nWyoming<\/td>\n134<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
\n

Question 1<\/h3>\n

1) What is the mean you calculated using the data analysis tool?<\/p>\n<\/div>\n

\n

Question 2<\/h3>\n

2) What does the mean represent in this context?<\/p>\n<\/div>\n

\n

Question 3<\/h3>\n

3) We are going to see how far above and below the mean the average daily screen\u00a0 time (in minutes) is for some states. In order to find this difference, use the following\u00a0 formula:<\/p>\n

Difference = (average daily screen time, in minutes) \u2013 (mean)<\/p>\n

For example, for Alabama, we would take the average daily screen time (170) and\u00a0 subtract the mean (178): 170 \u2013 178 = \u20138<\/p>\n

a) Find the difference between Oregon and the mean.<\/p>\n

b) Describe what this difference represents in this context.<\/p>\n

c) Find the difference between Michigan and the mean.<\/p>\n

d) Describe what this difference represents in this context.<\/p>\n<\/div>\n

\n

Question 4<\/h3>\n

4) If you live in a different state than the two above, find the difference between the\u00a0 state you live in and the mean. Describe what the difference represents in this\u00a0 context.<\/p>\n<\/div>\n

\n

Question 5<\/h3>\n

5) Consider the equation [latex]a=b[\/latex]. You can rewrite this equation in an equivalent form that has 0 on the right side by subtracting [latex]b[\/latex] from both sides, as follows:<\/p>\n

[latex]a=b[\/latex]<\/p>\n

[latex]a-b=b-b[\/latex]<\/p>\n

[latex]a-b=0[\/latex]<\/p>\n

a) Consider the equation [latex]\\mu_{1}=\\mu_{2}[\/latex]. Rewrite this equation in an equivalent form that has 0 on the right side by subtracting [latex]\\mu_{2}[\/latex] from both sides.<\/p>\n

b) Consider the inequality [latex]\\mu_{1}<\\mu_{2}[\/latex]. Rewrite this inequality in an equivalent form that has 0 on the right side by subtracting [latex]\\mu_{2}[\/latex] from both sides.\n\nc) Consider the inequality [latex]\\mu_{1}>\\mu_{2}[\/latex]. Rewrite this inequality in an equivalent form that has 0 on the right side by subtracting\u00a0[latex]\\mu_{2}[\/latex] from both sides.<\/p>\n<\/div>\n

\n

Question 6<\/h3>\n

6) Provide plausible values for the population mean that would make the following statements true.<\/span><\/p>\n

a) [latex]\\mu_{1}-\\mu_{2}=0[\/latex]<\/p>\n

b) [latex]\\mu_{1}-\\mu_{2}<0[\/latex]\n\nc) [latex]\\mu_{1}-\\mu_{2}>0[\/latex]<\/p>\n<\/div>\n

\n

Question 7<\/h3>\n

7) The formula for the test statistic to compare two population means contains multiple\u00a0 values for the sample mean, sample standard deviation, sample size, and population\u00a0 mean. To prepare for the preview assignment and in-class activity, match each symbol in the following table with its description by drawing lines between them.<\/p>\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Symbol<\/td>\n<\/td>\nDescription<\/td>\n<\/tr>\n
[latex]s_{1}[\/latex]<\/td>\n<\/td>\ndifference between the population means<\/td>\n<\/tr>\n
[latex]n_{1}[\/latex]<\/td>\n<\/td>\npopulation mean of Group 1<\/td>\n<\/tr>\n
[latex]\\bar{x}_{2}[\/latex]<\/td>\n<\/td>\nsample standard deviation of Group 1<\/td>\n<\/tr>\n
[latex]\\mu_{2}[\/latex]<\/td>\n<\/td>\nsample size of Group 1<\/td>\n<\/tr>\n
[latex]\\mu_{1}-\\mu_{2}[\/latex]<\/td>\n<\/td>\nsample mean of Group 2<\/td>\n<\/tr>\n
[latex]s_{2}[\/latex]<\/td>\n<\/td>\ndifference between the sample means<\/td>\n<\/tr>\n
[latex]n_{2}[\/latex]<\/td>\n<\/td>\nsample mean of Group 1<\/td>\n<\/tr>\n
[latex]\\mu_{1}[\/latex]<\/td>\n<\/td>\npopulation mean of Group 2<\/td>\n<\/tr>\n
[latex]\\bar{x}_{1}-\\bar{x}_{2}[\/latex]<\/td>\n<\/td>\nsample size of Group 2<\/td>\n<\/tr>\n
[latex]\\bar{x}_{1}[\/latex]<\/td>\n<\/td>\nsample standard deviation of Group 2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
  1. Wilkinson, D. (n.d.). Screen time trends in the age of COVID-19. SimpleTexting.\u00a0 https:\/\/simpletexting.com\/screentime-smartphone-usage-statistics\/ ↵<\/a><\/li><\/ol><\/div>","protected":false},"author":23592,"menu_order":7,"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-4937","chapter","type-chapter","status-publish","hentry"],"part":4875,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4937","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":5,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4937\/revisions"}],"predecessor-version":[{"id":5443,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4937\/revisions\/5443"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/4875"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4937\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=4937"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=4937"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=4937"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=4937"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}