Question

Time to Finish in 2012 Olympic Men’s Marathon In the 2012 Olympic Men’s Marathon, 85 athletes finished the race. Their times are stored in the file OlympicMarathon. Use the times stored in the Minutes column.

B.18 Time to Finish in 2012 Olympic Men's Marathon In the 2012 Olympic Men's Marathon, 85 athletes finished the race. Their times are stored in the file OlympicMarathon. Use the times stored in the Minutes column. (a) Use StatKey, other technology, or a random number table to randomly select 10 values. Indi- cate which values you've selected and compute the sample mean. (b) Repeat part (a) by taking a second sample and calculating the mean. Make a mini-dotplot by plotting the two sample means on a dotplot. (c) Find the mean for the entire population of 76 race times Use correct notation for vour answer Comment on the accuracy of using the sample means found in parts (a) and (b) to estimate the population mean. (d) Suppose we take many samples of size 10 from this population of values and plot the mean pe and center of the result. Draw a rough sketch of for each sample on a dotplot. Describe the sha a possible distribution for these means.

Answer 1

Kindly refer ot the attachment for solution .

I have taken the data from wikipedia page of 2012 marathon.

I have created two simulations in which i generated random numbers from 0 to 5 and took the number which counted for 10 times. (3 in sim1 an 2 in sim2).

Simulation1 Simulation2 Random Random Name Nationality Time(Hrs) Time(Min)number time(min) number Time(min) generator generator 1 Stephen Kiprotich 2 Abel Kirui 3 Wilson Kipsang Kiprotich 4 Mebrahtom Keflezighi 5 Marilson Dos Santos 6 Kentaro Nakamoto 7 Cuthbert Nyasango 8 Paulo Roberto Paula 9 Henryk Szost 2:08:01 2:08:27 2:09:37 2:11:06 128.02 128.02 Kenya Kenya United States Brazil Japan Zimbabwe Brazil Poland taly Switzerland Ukraine Brazil Russia Zimbabwe Australia 129.62 131.10 131.27 132.13 132.28 132.47 132.75 132.80 132.93 2:12:08 1 2:12:28 2:12:45 2:12:48 2:12:56 2:13:35 10 Ruggero Pertile 11 Viktor Röthlin 12 Oleksandr Sitkovskyy 13 Franck De Almeida 14 Aleksey Reunkov 15 Wirimai Juwawo 16 Michael Shelley 17 Emmanuel Kipchirchir Muta Kenya 18 Rachid Kisri 19 Yared Asmerom 1 1 133.82 134.15 134.15 2:14:10 135.15 135.40 Morocco Eritrea Canada Peru Canada Russia 2:15:09 2:15:24 2:15:26 2:15:35 2:16:00 2:16:04 21 Raúl Pacheco 135.58 136.00 136.07 136.28 136.42 136.47 136.48 136.48 136.60 137.00 135.58 23 Dmitriy Safronov 24 Carles Castillejo 25 laroslav Musinschi 26 Marius lonescu 27 Reid Coolsaet 28 Martin Dent 29 Vitaliy Shafar 30 Lee Merrien 31 Ignacio Cáceres 32 Lee Duhaeng 33 Faustine Mussa 34 José Carlos Hernández 1 Moldova Romania Canada Australia Ukraine Great Britain 136.42 2:16:28 2:16:29 136.48 136.48 2:17:00 South Korea Tanzania 137.32 137.65 137.80 2:17:19 137.32 137.65 137.80 2:17:48

144.2 65 César Lizano 66 Samson Ramadhani 67 Jan Kreisinger 68 Mohammed Abduh Bakhet Qatar 69 Jussi Utriainen 70 Arturo Malaquias 71 Wissem Hosni 72 Tamás Kovács 73 Jang Sinkweon 74 Toni Bernadó 75 Marcel Tschopp 76 Bekir Karayel 77 Chang Chia-Che 78 Ram Singh Yadav 79 Jean Pierre Mvuyekure 80 Konstantinos Poulios 81 Zohar Zimro 82 Jeong Jinhyeok 83 Juan Carlos Cardona 84 Augusto Soares 85 Tsepo Ramonene Costa Rica Tanzania Czech Republic 2:24:16 2:24:53 2:25:03 2:25:17 2:26:25 2:26:37 2:26:43 2:27:48 2:28:20 2:28:34 2:28:54 2:29:38 2:29:58 2:30:06 2:30:19 2:33:17 2:34:59 2:38:45 2:40:13 2:45:09 144.2 144.88 145.05 145.28 146.42 146.62 146.72 147.80 148.33 148.5 148.90 149.63 149.9 150.10 150.32 153.28 154.98 158.75 160.22 165.15 175.90 140.17 Finland Mexico Tunisia Hungary South Korea Andorra Liechtenstein 4 Chinese Taipei India Rwanda Greece Israel South Korea Colombia East Timor Lesotho Mean 160.22 4 139.7815 Mean frequen 137.11 137 mean 139 137 Horizontal Dot plot Accuracy(sample mean-pop 0.28% 2.20% mean mean % sample1 sample2