MGT 233 Homework #3, Spring 2018

Transcription

1 MGT 233 Homework #3, Spring 2018 This homework assignment is due at the beginning of class on March 30, Instructions: Download the MGT 233 Homework 3 Excel Data.xlsx from the MGT 233 website. Use the appropriate table to create the Excel Descriptive statistics. You must print the output of the descriptive statistics as part of your homework. Answer all parts clearly with proper probability notation and interpretation. Problem #1. History.teamusa.org - The number of medals won by the United States Winter Olympic Team in a sample of the winter sports is presented below. This includes gold, silver, and bronze medals won by both women and men in the Winter Olympics through the 2018 Pyeongchang games. Assume that the number of medals won per sport is normally distributed. Solve the following problem by hand using the equations on the equation sheet. Round all work to three decimal places. Sport # of Medals Alpine Skiing 47 Bobsled 25 Curling 2 Figure Skating 51 Freestyle Skiing 25 Ice Hockey 17 Luge 6 Nordic Combined 4 Skeleton 8 Snowboarding 31 Speedskating- Long Track 68 Speedskating- Short Track 20 A. Compute the mean and standard deviation of the number of medals won per sport. B. At 99% confidence, what is the margin of error? C. Compute and interpret a 99% confidence interval for the average number of medals won.

2 Problem #2. Pyeongchang2018.com - There were 93 different countries and republics represented at the 2018 Pyeongchang Winter Olympics. The following is a sample of the countries and republics with their respective number of participating athletes: Country Athletes Country Athletes Country Athletes Albania 2 Great Britain 59 New Zealand 21 Andorra 5 Greece 4 Nigeria 3 Argentina 6 Hungary 19 Norway 109 Armenia 3 Iceland 5 Olympic Athlete from Russia 168 Australia 51 India 2 Pakistan 2 Austria 105 Ireland 5 People's Republic of China 81 Azerbaijan 1 Israel 10 Philippines 2 Belgium 21 Italy 122 Poland 62 Bermuda 1 Jamaica 3 Portugal 2 Bolivia 2 Japan 124 Puerto Rico 1 Brazil 9 Kazakhstan 46 Republic of Korea 122 Bulgaria 21 Kenya 1 Romania 27 Canada 227 Kyrgyzstan 2 San Marino 1 Chile 7 Lebanon 3 Serbia 4 Colombia 4 Liechtenstein 3 Slovakia 56 Croatia 19 Lithuania 9 Slovenia 71 Czech Republic 95 Luxemburg 1 Spain 12 Denmark 17 Madagascar 1 Sweden 119 Ecuador 1 Malaysia 2 Switzerland 169 Eritrea 1 Malta 1 Thailand 4 Finland 106 Mexico 4 Togo 2 France 107 Monaco 4 Tonga 1 Georgia 4 Mongolia 2 Turkey 8 Germany 157 Montenegro 3 United States of America 243 Ghana 1 Morocco 2 Uzbekistan 2 Print the descriptive statistics in Excel and use the information to complete this problem. A. At 95% confidence, what is the margin of error? B. Compute and interpret a 95% confidence interval estimate for the average number of athletes participating in the Winter Olympics by country. C. Compute and interpret a 99% confidence interval estimate for the average number of athletes participating in the Winter Olympics by country.

3 Problem #3 Olympic.org - Scores for the singles figure skating competition are based on two events the short program and the free skate. The following list is a sample of the top finishers in the Men s Singles Figure Skating competition at the 2018 Pyeongchang Winter Olympics. Assume the population is normally distributed. Skater Score Adam Rippon Alexei Bychenko Cha Junhwan Daniel Somahin Dmitri Aliev Javier Fernandez Jin Boyang Jorik Hendrickx Keegan Messing Keiji Tanaka Michal Brezina Mikhail Kolyada Misha Ge Nathan Chen Patrick Chan Shoma Uno Vincent Zhou Yuzuru Hanyu Print the descriptive statistics in Excel and use the information to complete this problem. A. Compute and interpret a 90% confidence level for the average total score per male Olympic figure skater. B. Compute and interpret a 95% confidence level for the average total score per male Olympic figure skater. C. Compute and interpret a 99% confidence level for the average total score per male Olympic figure skater.

4 Problem #4. olympic.org/biathlon - The word biathlon stems from the Greek word for two contests, and is today seen as the joining of two sports; skiing and shooting. Biathlon has its roots in survival skills practiced in the snow-covered forests of Scandinavia, where people hunted on skis with rifles slung over their shoulders. The Biathlon made its Olympic debut at the 1960 Squaw Valley Winter Games. The following is a sample of times for the Women s 10KM Pursuit at the 2018 Pyeongchang Winter Olympics. Participant Time (Min) Participant Time (Min) Anais Bescond Kaisa Makarainen Anais Chevalier Krystyne Guzik Anastasiya Kuzmina Laura Dahlmeier Baiba Bendika Lena Haecki Darya Domracheva Linn Persson Denise Herrmann Liza Vittozzi Dorothea Wierer Marie Dorin Habert Elisa Gasparin Marketa Davidova Elisabeth Hoegberg Marte Olsbu Eva Puskarcikova Mona Brorsson Franziska Hildebrand Nadezhda Skardino Galina Vishnevskaya Paulina Failkova Hanna Oeberg Rosanna Crawford Irene Cadurisch Tatiana Akimova Iryna Kryuko Tiril Eckhoff Jessica Jislova Vanessa Hinz Johanna Talihaerm Veronika Vitkova Julia Ransom Vita Semerenko Justine Braisaz Weronika Nowakowska Print the descriptive statistics in Excel and use the information to complete this problem. A. Compute and interpret an 80% confidence interval estimate for the average time of the women s 10KM Pursuit race. B. Compute and interpret a 90% confidence interval estimate for the average time of the women s 10KM Pursuit race. C. Compute and interpret a 95% confidence interval estimate for the average time of the women s 10KM Pursuit race.

5 Problem #5. Parade.com - According to Bridgestone s Winter Driving Survey, in a survey of 100 Americans, 76% watch the Winter Olympics. With 80% confidence, the Bridgestone survey team claims there is a margin of error of 5.5%. A. Was the survey team accurate in reporting a 5.5% margin of error? Show work by carrying the answer to 4 decimal places. B. What sample size is needed for a margin of error of 5% with 90% confidence? C. What sample size is needed for a margin of error of 3% with 95% confidence? D. What sample size is needed for a margin of error of 1% with 98% confidence? Problem #6. Teamusa.org Team USA consisted of 243 athletes for the 2018 Pyeongchang Winter Olympics. In a sample of 98 Winter Olympic athletes, 56 were male. Use this information for the following: A. Compute and interpret an 80% confidence interval for the proportion of male Winter Olympic athletes. B. Compute and interpret a 99% confidence interval for the proportion of male Winter Olympic athletes. Problem #7. History.teamusa.org - In the Winter Olympics, Norway has been awarded the highest number of medals. In second place is the United States. The medals that the United States has won includes the following composition: 34.20% gold, 36.16% silver, and 29.64% bronze. A. What sample size is needed to estimate the proportion of total gold medals won by the United States using a 2% margin of error and assuming a 99% confidence level. B. What sample size is needed to estimate the proportion of total silver medals won by the United States using a 5% margin of error and assuming a 98% confidence level.

6 Problem #8. Washingtonpost.com - The Winter Olympics are relatively short compared to the Summer Olympics, perhaps because it encompasses some of the speediest competitions of any sport. For example, in the most recent world championships, the luge winner averaged 81.3 mph, followed by the four-man bobsled, 78.7 mph, and the skeleton, 71.9 mph. In the 2018 Pyeongchang Winter Olympics, a sample of 40 male luge and 35 male skeleton racers was observed. In a sample of participants in the luge, the average speed was mph with a standard deviation of 2.98 mph. The average speed of the sample of participants in the skeleton was mph with a standard deviation of 1.23 mph. A. What is the point estimate of the difference between the average speed of skeleton participants and luge participants? B. What is the 90% confidence interval for the difference between the average speed of skeleton participants and luge participants? Interpret the results. C. Suppose you want to estimate the average speed of women skeleton racers. Historically, the standard deviation of female skeleton racers is about the same as that of male skeleton racers. If you are seeking a 99% confidence level and a margin of error of 1.2 mph, what sample size do you need? Problem #9. Olympic.org - In a sample of 1,677 male winter Olympic athletes, 35.2% are 30 years or older. However, in a sample of 1,242 female winter Olympic athletes, only 20.2% are 30 years or older. A. Using a 90% confidence interval, evaluate the difference between the percent of male versus female Olympic athletes that are at least 30 years old. Interpret your results.