Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Statistics Individual – January 16, 2016 – FAMAT State-Wide Competition hosted by Vero Beach HS 1. Swimming is one of the major sports in the Summer Olympics. Using the table given below, find the women’s event from 2012 with the largest spread in actual times for the event: A. B. C. D. E. 50 Free 200 IM 800 Free 100 Back None of these Answers 2. Synchronized swimming is a fairly new sport to the Summer Olympics, it began in 1984 in Los Angeles. It was replaced in 1996 by water ballet. Since the 2000 games, it has been included. Along with Rhythmic gymnastics, it is the only sport exclusively for women in the Olympics. The first Olympics in the Modern Era was in 1896 in Athens, Greece. Assuming there was an Olympics every four years since then, find the probability that Synchronized Swimming was an event at any selected Summer Olympics including Rio 2016. A. 8⁄31 B. 7⁄31 C. 4⁄15 D. 7⁄30 E. None of these Answers 3. In Olympic diving, the springboard is a flexible diving board that can be adjusted to create more or less spring. It must be at least 4.8 meters long and a half-meter wide. The springboards being used at the 2016 Rio Summer Olympics have a known mean spring of 30 cm and a standard deviation of 1.8 cm. Assuming they have a normal distribution, find the spring length to the nearest tenth that represents the 84th percentile of springboards at the 2016 Rio Olympics. A. 28.2 cm D. 33.8 cm B. 31.8 cm E. None of these Answers C. 33.6 cm 4. Using the Scatterplot below, as well as the line of best fit that is drawn onto it, name the country best described as an influential observation: A. China B. Japan C. USA D. Germany E. None of these Answers 1 Statistics Individual – January 16, 2016 – FAMAT State-Wide Competition hosted by Vero Beach HS 5. Using the graph provided, choose the best answer: A. The association between time and the year appears to have a positive association for the Men’s 100m Freestyle. B. The correlation between time and the year appears to be weak for the Men’s 100 m Freestyle. C. Using this information to predict times for 2016 Olympics would be interpolation. D. The correlation of time and the year for the Men’s 100m Freestyle appears to be closer -1 than 1. E. None of these Answers the to 6. Tom Brady wants to join the US Olympic Water Polo team. The ball used in water polo weighs between 400 and 450 grams. If Tom prefers his game ball slightly underinflated at the 8th percentile, what is the mass in grams of the ball Tom prefers? Assume the balls follow a normal distribution. Round to the nearest ten grams. A. 400 D. 440 B. 410 E. None of these Answers C. 420 7. Using this _______, you should be able find the Country with the largest percentage of silver medals to be ____. A. Segmented Bar Chart, China B. Segmented Bar Chart, Germany C. Histogram, China D. Frequency Diagram, Russia E. None of these Answers to 8. Using the scatterplot below, describe the direction, form and strength of the relationship between training hours and calories for Olympic swimmers. A. B. C. D. E. Positive direction, Linear, Somewhat weak Positive direction, Non-Linear, Strong Negative direction, Linear, Somewhat weak Positive direction, Non-Linear, Very Strong None of these Answers 2 Statistics Individual – January 16, 2016 – FAMAT State-Wide Competition hosted by Vero Beach HS 9. The data on one Olympic Swimming event is given in the table below. Use the data to write the Least Squares Regression Line the time to finish the race as a function of the years past 1920. What point is guaranteed to be on the regression line? Round values to the nearest hundredth. A. (4, 362.2) B. (44.22, 284.41) C. (44, 283.30) D. No points are guaranteed to be on the line E. None of these Answers for 10. A synchronized swimmer can hold their breath up to 3 minutes on average. To give you perspective, a dolphin can hold their breath about 9 minutes, and a grey seal can hold theirs about an hour and a half. A sample was taken of Olympic synchronized swimmers and their time holding their breath recorded. What are the outliers in this sample? Use the IQR Method to determine. All times measured in seconds. 28, 165, 168, 170, 172, 190, 192, 195, 202, 220 A. B. C. D. IQR=27 and the Outlier is 220 IQR=192 and the Outlier is 28 IQR=27 and there are no Outliers IQR=192 and there are no Outliers E. None of these Answers 11. Competitive diving, which developed from gymnastics, started in Sweden and Germany in the 18th century. Known as the greatest diver of all time, American Greg Louganis is “board” one day and takes a sample of his times to hit the water from the diving board. Using the sample of times (in seconds) given below, find the appropriate measure of spread for the distribution. 0.121 , 0.234 , 0.367 , 0.444 , 0.512 , 0.676 , 0.876 , 0.888 , 0. 904 , 0.924 , 1.001 , 1.245 A. M=0.776 because the distribution is symmetric B. M=0.776 because the distribution is leftskewed C. 𝑥̅ = 0.683 because the distribution is not symmetric 12. What can be concluded from the chart below about Michael Phelps? A. Michael Phelps won twice the number of gold medals between 2004-2012 as the United Kingdom. B. Michael Phelps won more gold medals from 2004-2012 than exactly 8 countries. D. 𝑥̅ = 0.683 because the distribution is left-skewed E. None of these Answers 3 Statistics Individual – January 16, 2016 – FAMAT State-Wide Competition hosted by Vero Beach HS C. This is a bar chart because the medalists is a qualitative variable. D. Michael Phelps is in the 45th percentile for gold medals in 2004-2012. E. None of these Answers 13. Speaking of Michael Phelps, the following modified box and whisker plot shows how fast one of the world's greatest Olympic swimmers, has swum the 200-meter freestyle event (rounded to the nearest second). Which of the following is NOT correct according to the data below? A. 108 seconds is the Upper Quartile. B. The Interquartile Range of the distribution is less than 4 seconds. C. 103 is the Lower Quartile and the minimum value. D. There are no outliers in this distribution. E. None of these Answers 14. Using the data table, find the probabilities: 2016 Olympians Swimming USA China Russia 88 75 90 A. B. C. 497 1275 56 497 521 1275 Diving Synchronized Swimming 24 16 28 20 20 32 𝑃(𝑈𝑆𝐴|𝐷𝑖𝑣𝑖𝑛𝑔) + 𝑃(𝑊𝑎𝑡𝑒𝑟 𝑃𝑜𝑙𝑜) D. Water Polo 15 15 2 99 497 E. None of these Answers 15. Using the information from the table on problem 14, determine if the number of Olympic athletes in each sport is independent of country. Choose the best answer below. A. Yes, because the country you are from does not affect the sport you play. B. Yes, because the country you are from does affect the sport you play. C. No, because the probabilities of playing each sport are equal for each country. D. No, because the probabilities of playing each sport are different for each country. E. None of these Answers 16. Water polo made its Olympic debut at the Paris Games in 1900. It was not included in 1904 but would be present at each subsequent edition of the Olympic Games. Since then, the Hungarians have been by far the greatest ambassadors of this discipline. Between 1928 and 1980, they won medals at every Games. Between 1932 and 1976, they even won six of the 10 gold medals available. In 2000 in Sydney, Hungary make a remarkable comeback, winning its seventh gold medal in water polo. In the same year, women’s water polo made its first official appearance at the Olympic Games, 100 years after the debut of this discipline. From the paragraph above, choose the best example of a quantitative variable: A. 1928 B. Water Polo C. Olympic Games D. Number of Gold Medals E. None of these Answers 4 Statistics Individual – January 16, 2016 – FAMAT State-Wide Competition hosted by Vero Beach HS 17. Women’s swimming became Olympic in 1912 at the Stockholm Games. Since then, it has been part of every edition of the Games. The men’s and women’s programs are almost identical, as they contain the same number of events, with only one difference: the freestyle distance is 800 meters for women and 1,500 meters for men. Can the two sets of all events for men and women swimmers (their programs) in the Olympics be considered disjoint? Explain why or why not. A. Yes, men and women can’t swim in the same events, so they must be disjoint. B. Yes, because the freestyle distance is different for men and women. C. No, most of the events for men and women swimmers are the same. D. No, men can race in more than one event. E. None of these Answers 18. For Olympic Synchronized swimming, the pool must be a minimum of 20 m by 30 m, and within that a 12 m by 12 m area must be at least 3 m deep. The water temperature must be 26 degrees Celsius, plus or minus one degree. If Olympic pools for synchronized swimming have a normal distribution with a 27 degree Celsius pool having a z score of 3, find the maximum temperature of the pool in the 92nd percentile. Round to the nearest hundredth degree Celsius. A. 26.47 D. 31.22 B. 27.47 E. None of these Answers C. 30.22 19. Which of the following is NOT true about this graph? A. The legend is labeled as “Gold Medals” indicating the bars in the bar graph represent gold medals awarded to each country. B. The area principle is violated on this graph to make United States appear superior. C. The y-axis is missing a label, but we know the numbers represent frequency in a bar graph. D. The countries listed on the x-axis of the graph represent the categorical variable “Country”. E. None of these Answers 20. Use the following table to determine if there is a correlation between Total Swim Time and Ave Swim Pace. Describe the relationship. 5 Statistics Individual – January 16, 2016 – FAMAT State-Wide Competition hosted by Vero Beach HS A. The relationship is very non-linear. The correlation is weak at -0.33. There is almost no association between total swim time and their average swim pace. B. The relationship is fairly linear. The correlation is weak at -0.33. There is little association between total swim time and their average swim pace. C. The relationship is fairly linear. The correlation is -0.90 seconds. There is an association between total swim time and their average swim pace. D. The relationship is fairly linear. The correlation is -0.90. There is a linear association between total swim time and their average swim pace. E. None of these Answers 6 Statistics Individual – January 16, 2016 – FAMAT State-Wide Competition hosted by Vero Beach HS Solutions: 1 B or C 2A 3B 4C 5D 6 A or B 7 B or E 8A 9B 10 E 11 E 12 C 13 A 14 C 15 D 16 D 17 A or C 18 A 19 B 20 D You can see from the table provided that the largest standard deviation is 3.28. By looking at the arithmetic sequence, the following equation can be used to find the number of Olympic Games since 1896. 2016 = 1896 + 4𝑥; 𝑥 = 30 That makes 31 games total, and 8 with Synchronized Swimming (1984, 1988, 1992, 2000, 2004, 2008, 2012, 2016) The probability is then 8/31. By using the empirical rule, the 84th percentile is exactly one standard deviation about the mean. 30+1.8=31.8 cm Influential Observations are defined to be extreme outliers in the x-direction. They pull the line of best fit towards them. The correlation between the variables is most likely negative because of the direction of the data points. Knowing the area to the left of the data value is 8%, the mean is 425, and SD is 25/3, we can use the INVnorm function on the calculator to find: X=413.3, but rounded to the nearest ten is 410. Germany has 19/44=43% silver medals. Positive direction is because as the x’s go up, so do the y’s for the majority of values, Linear because is follows a fairly linear pattern, Somewhat weak because the correlation will most likely be low. The point (x bar, y bar) is guaranteed to be on the Least Squares Regression Line. Find the average of each list and that point is (44.22, 284.41). The IQR is 27, which makes the outlier 28. M=0.776 because the distribution is left-skewed. Any time that a distribution is skewed, the proper measure of center is the median. You can tell this distribution is left-skewed because the box plot is larger on the left side of the median. Also, the median is more than the mean, which indicates the mean is being pulled to the tail on the left. (Median is not a measure of spread) This is a bar chart because the variable of interest is qualitative. Histograms are used for quantitative data. 108 is the maximum. 24/72 + 32/425=521/1275 (To find a probability of USA given Diving, you find the number of athletes who are from the USA who dive, and then divided by the number who are Divers. Because all of the conditional probabilities do not match, the variables are NOT independent. Quantitative variables are numerical values that describe an individual. The events for men and women are almost identical. Therefore they cannot be disjoint, where there are no events that overlap. To find the mean, you use the information given and it is 26. To find the standard deviation, use the z27−26 score given to solve: 3 = 𝜎 Invnorm(0.92,26,1/3)=26.468 The area principle says that all values on a graph should be in their true proportions. There is a consistent scale on the graph so that is not an issue. By using the linreg function on the calculator, I found the correlation to be -0.90. The scatterplot looks like a negative linear association. “C” is incorrect because the units on the correlation. 7