{"id":5049,"date":"2022-08-17T19:52:49","date_gmt":"2022-08-17T19:52:49","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5049"},"modified":"2022-08-23T21:06:22","modified_gmt":"2022-08-23T21:06:22","slug":"13d-inclass","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/13d-inclass\/","title":{"raw":"13D InClass","rendered":"13D InClass"},"content":{"raw":"[caption id=\"\" align=\"alignright\" width=\"314\"]\"A Credit: iStock\/PeopleImages[\/caption]\r\n\r\nThe study in this in-class activity uses a single\u00a0group of participants and measures their\u00a0reaction times (in milliseconds) while\u00a0performing a driving task without using their\u00a0cell phones and then again while using their\u00a0cell phones.[footnote]Strayer, D. L. & Johnston, W. A. (2001, November 1). Driven to distraction: Dual-task studies of\u00a0 simulated driving and conversing on a cellular telephone. Psychological Science, 12(6), 462\u2013466. DOI:\u00a0 10.1111\/1467-9280.00386[\/footnote]\r\n\r\nWe will use statistical inference to compare\u00a0reaction times for the two conditions (using\u00a0and not using cell phones).\r\n\r\n \r\n\r\n \r\n
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Question 1<\/h3>\r\n1) Do you think a driver\u2019s reaction time is different when they are using a cell phone as\u00a0 opposed to when they are not using a cell phone while driving?\r\n\r\n<\/div>\r\nThe data collected include the reaction times (in milliseconds) with and without the use\u00a0 of cell phones for 32 randomly selected participants. The data for the first 10\u00a0 participants are displayed in the following table.\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
Participant<\/td>\r\nReaction Time (in milliseconds)<\/td>\r\n<\/tr>\r\n
Cell Phone Use = Yes<\/td>\r\nCell Phone Use = No<\/td>\r\n<\/tr>\r\n
1<\/td>\r\n636<\/td>\r\n604<\/td>\r\n<\/tr>\r\n
2<\/td>\r\n623<\/td>\r\n556<\/td>\r\n<\/tr>\r\n
3<\/td>\r\n615<\/td>\r\n540<\/td>\r\n<\/tr>\r\n
4<\/td>\r\n672<\/td>\r\n522<\/td>\r\n<\/tr>\r\n
5<\/td>\r\n601<\/td>\r\n459<\/td>\r\n<\/tr>\r\n
6<\/td>\r\n600<\/td>\r\n544<\/td>\r\n<\/tr>\r\n
7<\/td>\r\n542<\/td>\r\n513<\/td>\r\n<\/tr>\r\n
8<\/td>\r\n554<\/td>\r\n470<\/td>\r\n<\/tr>\r\n
9<\/td>\r\n543<\/td>\r\n556<\/td>\r\n<\/tr>\r\n
10<\/td>\r\n520<\/td>\r\n531<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n
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Question 2<\/h3>\r\n2) In order to use the study data to compare reaction times for the two conditions\u00a0 (using and not using cell phones) using statistical inference, we must determine if\u00a0 the two samples are dependent (paired) or independent samples. Analyze the\u00a0 context of the study and determine if the samples are dependent or independent\u00a0 samples. Explain.\r\n\r\n<\/div>\r\nIn order to compare the reaction times for dependent samples, we first calculate the difference between the reaction time of each participant with the use of a cell phone and\u00a0 without the use of a cell phone.\r\n\r\nThe reaction times of a participant performing the same driving task with and without the use of a cell phone in a randomly decided order are recorded in the following table. The\u00a0 difference is defined by:\r\n\r\nDifference = (reaction time with the use of a cell phone) \u2013 (reaction time without the use\u00a0 of a cell phone)\r\n
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Question 3<\/h3>\r\n3) Calculate the missing difference for Participant 1 between the reaction times\u00a0 performing the same driving task with and without the use of a cell phone.\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\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Participant<\/td>\r\nReaction Time (in Milliseconds)<\/td>\r\nDifference<\/td>\r\n<\/tr>\r\n
Cell Phone Use = Yes<\/td>\r\nCell Phone Use = No<\/td>\r\n<\/tr>\r\n
1<\/td>\r\n636<\/td>\r\n604<\/td>\r\n<\/td>\r\n<\/tr>\r\n
2<\/td>\r\n623<\/td>\r\n556<\/td>\r\n67<\/td>\r\n<\/tr>\r\n
3<\/td>\r\n615<\/td>\r\n540<\/td>\r\n75<\/td>\r\n<\/tr>\r\n
4<\/td>\r\n672<\/td>\r\n522<\/td>\r\n150<\/td>\r\n<\/tr>\r\n
5<\/td>\r\n601<\/td>\r\n459<\/td>\r\n142<\/td>\r\n<\/tr>\r\n
6<\/td>\r\n600<\/td>\r\n544<\/td>\r\n56<\/td>\r\n<\/tr>\r\n
7<\/td>\r\n542<\/td>\r\n513<\/td>\r\n29<\/td>\r\n<\/tr>\r\n
8<\/td>\r\n554<\/td>\r\n470<\/td>\r\n84<\/td>\r\n<\/tr>\r\n
9<\/td>\r\n543<\/td>\r\n556<\/td>\r\n-13<\/td>\r\n<\/tr>\r\n
10<\/td>\r\n520<\/td>\r\n531<\/td>\r\n\u221211<\/td>\r\n<\/tr>\r\n
11<\/td>\r\n609<\/td>\r\n599<\/td>\r\n10<\/td>\r\n<\/tr>\r\n
12<\/td>\r\n559<\/td>\r\n537<\/td>\r\n22<\/td>\r\n<\/tr>\r\n
13<\/td>\r\n595<\/td>\r\n619<\/td>\r\n\u221224<\/td>\r\n<\/tr>\r\n
14<\/td>\r\n565<\/td>\r\n536<\/td>\r\n29<\/td>\r\n<\/tr>\r\n
15<\/td>\r\n573<\/td>\r\n554<\/td>\r\n19<\/td>\r\n<\/tr>\r\n
16<\/td>\r\n554<\/td>\r\n467<\/td>\r\n87<\/td>\r\n<\/tr>\r\n
17<\/td>\r\n626<\/td>\r\n525<\/td>\r\n101<\/td>\r\n<\/tr>\r\n
18<\/td>\r\n501<\/td>\r\n508<\/td>\r\n\u22127<\/td>\r\n<\/tr>\r\n
19<\/td>\r\n574<\/td>\r\n529<\/td>\r\n45<\/td>\r\n<\/tr>\r\n
20<\/td>\r\n468<\/td>\r\n470<\/td>\r\n\u22122<\/td>\r\n<\/tr>\r\n
21<\/td>\r\n578<\/td>\r\n512<\/td>\r\n66<\/td>\r\n<\/tr>\r\n
22<\/td>\r\n560<\/td>\r\n487<\/td>\r\n73<\/td>\r\n<\/tr>\r\n
23<\/td>\r\n525<\/td>\r\n515<\/td>\r\n10<\/td>\r\n<\/tr>\r\n
24<\/td>\r\n647<\/td>\r\n499<\/td>\r\n148<\/td>\r\n<\/tr>\r\n
25<\/td>\r\n456<\/td>\r\n448<\/td>\r\n8<\/td>\r\n<\/tr>\r\n
26<\/td>\r\n688<\/td>\r\n558<\/td>\r\n130<\/td>\r\n<\/tr>\r\n
27<\/td>\r\n679<\/td>\r\n589<\/td>\r\n90<\/td>\r\n<\/tr>\r\n
28<\/td>\r\n960<\/td>\r\n814<\/td>\r\n146<\/td>\r\n<\/tr>\r\n
29<\/td>\r\n558<\/td>\r\n519<\/td>\r\n39<\/td>\r\n<\/tr>\r\n
30<\/td>\r\n482<\/td>\r\n462<\/td>\r\n20<\/td>\r\n<\/tr>\r\n
31<\/td>\r\n527<\/td>\r\n521<\/td>\r\n6<\/td>\r\n<\/tr>\r\n
32<\/td>\r\n536<\/td>\r\n543<\/td>\r\n\u22127<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n
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Question 4<\/h3>\r\n4) Describe the difference, in context, for Participant 32.\r\n\r\n<\/div>\r\n
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Question 5<\/h3>\r\n5) Look at the reaction times and the difference for Participant 8. Complete the\u00a0 following sentence by circling the correct word in parentheses.\r\n\r\n<\/div>\r\nThe reaction time for Participant 8 performing the same driving task was 84 milliseconds (shorter\/longer) with the use of a cell phone than without the use of a\u00a0 cell phone.\r\n
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Question 6<\/h3>\r\n6) Go to the DCMP Describing and Exploring Quantitative Variables tool at\u00a0 https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/. Locate the \u201cEnter Data\u201d drop-down menu and select \u201cYour Own.\u201d Copy and paste the numbers in the\u00a0 Difference column of the previous table.\r\n\r\nWrite down the sample mean difference and the sample standard deviation of the\u00a0 differences.\r\n\r\n<\/div>\r\nA dependent (paired) t-test compares the mean difference to a hypothesized value,\u00a0 which is often 0 (no difference). It is always important to check the assumptions of a test\u00a0 before you perform any calculations.\r\n
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Question 7<\/h3>\r\n7) Given the previous information, is a dependent t-test the appropriate method to use\u00a0 to answer the following research question: \u201cDoes a driver\u2019s reaction times (in\u00a0 milliseconds) differ when they are using a cell phone as opposed to when they are\u00a0 not using a cell phone?\u201d\r\n\r\n<\/div>\r\n
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Question 8<\/h3>\r\n8) Go to the DCMP Compare Two Means tool at https:\/\/dcmathpathways.shinyapps.io\/2sample_mean\/ and click on the tab Two\u00a0 Dependent Samples. Use the following inputs:\r\n