Athletes are interested to know whether their Transition 1 time from swim to bike in a sprint triathlon is the same as in a super sprint triathlon. Consider the 2013 male triathletes who competed in both the Individual Sprint Triathlon (sprint) and in the Team Relay Triathlon (super sprint) as a sample of all male triathletes. Details of their race times can be found in the Excel sheet “2013 Men Sprint & Super Sprint”. (Hint: The athlete’s individual performance in a Team Relay is their Super Sprint data.) a) Consider the differences for Transition 1 times between a sprint triathlon and a super sprint triathlon. (Hint: The sample data are matched pairs. Explain why.) Find the sample mean and sample standard deviation for the differences.   b) Is there enough evidence at the 10% significance level to conclude that the average Transition 1 time is different in a sprint than in a super sprint? (Hint: Use the results of a) and apply the t-test for difference of population means.) Provide a possible explanation for the difference you did or did not observe.   c) Estimate, with 90% confidence, the population mean difference in Transition 1 times between a sprint and super sprint. Interpret the result. (Hint: Use the results of a) to construct a confidence interval estimate using the t-distribution.) Athlete Information Sprint Super Sprint (Individual Result from Team Relay) Year First Last P/T Place Total Time Swim Transition 1 Bike Transition 2 Run Place Total Time Swim Transition 1 Bike Transition 2 Run 2013 Will Allan NS 23 1:01:14 0:11:03 0:00:50 0:32:33 0:00:37 0:16:11 9 0:20:49 0:03:59 0:00:37 0:10:29 0:00:41 0:05:04 2013 Cooper Bentley AB 13 0:58:50 0:09:37 0:00:42 0:31:13 0:00:37 0:16:41 3 0:20:16 0:03:14 0:00:36 0:10:40 0:00:38 0:05:01 2013 Robert Bigsby SK 5 0:56:15 0:08:52 0:00:42 0:29:41 0:00:34 0:16:26 5 0:19:32 0:03:07 0:00:33 0:10:21 0:00:38 0:04:55 2013 Reid Burrows NB 15 0:59:05 0:09:10 0:00:45 0:30:20 0:00:38 0:18:12 8 0:20:00 0:03:07 0:00:34 0:10:04 0:00:40 0:05:37 2013 Austen Forbes ON 7 0:56:42 0:08:55 0:01:05 0:30:18 0:00:36 0:15:48 2 0:19:43 0:03:15 0:00:36 0:10:31 0:00:37 0:04:45 2013 Connor Foreman BC 10 0:57:30 0:08:48 0:00:47 0:29:39 0:00:39 0:17:37 6 0:20:07 0:03:08 0:00:36 0:10:39 0:00:40 0:05:06 2013 Conor Gillespie-Friesen NS 3 0:55:35 0:08:51 0:00:41 0:29:44 0:00:36 0:15:43 9 0:19:10 0:02:59 0:00:36 0:09:59 0:00:38 0:05:00 2013 Peter Gregory NL 24 1:01:33 0:09:01 0:01:00 0:31:33 0:00:44 0:19:15 7 0:21:33 0:03:18 0:00:48 0:11:03 0:00:50 0:05:37 2013 Xavier Grenier-Talavera QC 1 0:55:13 0:08:46 0:00:45 0:29:41 0:00:34 0:15:27 1 0:18:52 0:03:05 0:00:34 0:09:53 0:00:38 0:04:45 2013 Darian Hole MB 16 0:59:12 0:09:32 0:00:51 0:31:08 0:00:38 0:17:03 4 0:20:50 0:03:30 0:00:40 0:10:36 0:00:48 0:05:17 2013 Sean Hooper SK 21 1:01:00 0:09:46 0:00:51 0:31:44 0:00:37 0:18:02 5 0:21:07 0:03:41 0:00:38 0:10:47 0:00:45 0:05:17 2013 Aidan Katz SK 25 1:02:17 0:08:59 0:00:54 0:32:28 0:00:38 0:19:18 5 0:20:49 0:03:15 0:00:34 0:10:58 0:00:39 0:05:24 2013 Carsten Lapointe BC 19 0:59:56 0:09:33 0:00:48 0:31:11 0:00:35 0:17:49 6 0:20:51 0:03:37 0:00:36 0:10:50 0:00:38 0:05:12 2013 Francis Lefebvre QC 8 0:56:51 0:08:53 0:00:40 0:29:39 0:00:34 0:17:05 1 0:19:40 0:03:22 0:00:34 0:10:22 0:00:38 0:04:47 2013 Alexis Lepage QC 11 0:57:45 0:08:47 0:00:46 0:30:47 0:00:37 0:16:48 1 0:19:56 0:03:08 0:00:37 0:10:09 0:00:44 0:05:21 2013 Alexander MacKay PEI 22 1:01:09 0:09:10 0:00:44 0:30:22 0:00:42 0:20:11 10 0:21:22 0:03:10 0:00:34 0:11:34 0:00:39 0:05:27 2013 Tyler Mislawchuk MB 2 0:55:26 0:08:46 0:00:45 0:29:41 0:00:33 0:15:41 4 0:19:02 0:03:01 0:00:35 0:09:53 0:00:38 0:04:56 2013 Aron Mohammadi ON 14 0:58:58 0:09:05 0:00:39 0:30:35 0:00:39 0:18:00 2 0:20:13 0:03:14 0:00:37 0:10:45 0:00:39 0:05:00 2013 Alex Neuffer PEI 26 1:02:40 0:11:25 0:00:58 0:32:46 0:00:43 0:16:48 10 0:21:04 0:04:02 0:00:39 0:10:59 0:00:43 0:04:44 2013 Jericho O'Connell BC 20 1:00:24 0:09:35 0:00:55 0:31:49 0:00:39 0:17:26 6 0:21:06 0:03:30 0:00:40 0:10:42 0:00:57 0:05:19 2013 Russell Pennock AB 6 0:56:24 0:08:50 0:00:55 0:30:34 0:00:37 0:15:28 3 0:19:21 0:03:05 0:00:37 0:10:21 0:00:35 0:04:45 2013 John Pexman AB 17 0:59:17 0:09:25 0:00:57 0:30:43 0:00:57 0:17:15 3 0:20:20 0:03:25 0:00:37 0:10:25 0:00:40 0:05:15 2013 Martin Sobey PEI 27 1:03:18 0:10:15 0:01:02 0:33:08 0:00:37 0:18:16 10 0:22:18 0:03:58 0:00:41 0:11:48 0:00:38 0:05:14 2013 Patrick Stewart NS 29 1:06:54 0:11:26 0:00:57 0:33:53 0:00:43 0:19:55 9 0:24:33 0:03:44 0:00:45 0:12:26 0:00:46 0:06:53 2013 Paul Tremblay NB 30 1:07:29 0:11:43 0:00:58 0:34:38 0:00:42 0:19:28 8 0:21:18 0:04:09 0:00:38 0:10:32 0:00:41 0:05:21 2013 Riley Unger MB 12 0:58:07 0:08:49 0:00:49 0:29:38 0:00:44 0:18:07 4 0:20:21 0:03:17 0:00:36 0:10:13 0:00:39 0:05:38 2013 Charles Waugh NB 28 1:05:50 0:09:31 0:01:20 0:34:25 0:00:46 0:19:48 8 0:22:51 0:03:36 0:00:40 0:12:04 0:00:48 0:05:44 2013 Marty Whelan NL 9 0:57:26 0:08:46 0:00:50 0:29:39 0:00:38 0:17:33 7 0:19:56 0:03:02 0:00:34 0:09:58 0:00:43 0:05:42 2013 Nathan Wilson NL 18 0:59:23 0:09:21 0:00:44 0:31:20 0:00:41 0:17:17 7 0:21:09 0:03:29 0:00:38 0:10:41 0:00:57 0:05:26 2013 Myles Zagar ON 4 0:56:04 0:08:46 0:00:45 0:29:42 0:00:39 0:16:12 2 0:19:44 0:03:04 0:00:34 0:09:54 0:00:41 0:05:3

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.