Statistics 101, Section 001: December 14, 2002Final ExamInstructions: Write your answers on the exam in the spaces after the questions. For maximum credit, show all work. Writing an answer without showing work may not receive full credit.You are permitted to use four sheets of paper filled with whatever information you put on them. Other notes, texts, or pieces of paper are not permitted. You cannot work with or ask questions of others. If you need clarification on any part of the exam, contact Prof. Reiter.Provide the information requested below in the adjacent empty spaces.NAME (print): LAB SECTION:Honor Pledge: ``I have not given or received assistance on this exam while taking the exam.''SIGNATURE:Page Points Possible Score3 184 125 156 157 158 159 2010 2011 20Total 1501QUESTIONS 1 – 17 REFER TO THE DATA SET DESCRIBED BELOWWhat factors are related to the formation of hurricanes and tropical storms? To assess this question, W. Gray (1998) gathered storm data for each year from 1950 to 1997. The variables include:--- The number of hurricanes in the year.--- The number of tropical storms in the year. (Tropical storms are serious but not quite hurricanes.)--- The value of a commonly used storm index score. A score of 100 is an average year, and a score above 100 is a year when storms are stronger than average. --- Whether West Africa experienced a wet or dry year.--- Whether the El Nino effect was cold, neutral, or warm. That is, whether the ocean temperatures in the Pacific were colder than usual, about the same as usual, or warmer than usual.There are no missing data, so that there are 48 observations.There are no problems on this page. The problems begin on the next page.Questions 1 – 10 and 13-17 are worth three points each.250 100 150 200 250Below are histograms for hurricanes, tropical storms, and storm index.Number of Hurricanes Number of Tropical Storms0 2 4 6 8 10 12 145 10 15 20Storm index QUESTIONS BEGIN HERE1. Order the three variables by the values of their standard deviations (SD). Write the variable name next to each choice.Largest SD: ___________In Between SD: ___________ Smallest SD: ___________2. Estimate the following quantities for number of hurricanes in a given year: Median: ________ Mean: _______ SD: _______ 3. Estimate the percentage of years that have between four and eight hurricanes. Include the years with four or eight in your estimate. ________4. True or False: The median storm index is larger than 100. 5. True or False: A normal probability plot for the storm index would show the points on an approximately straight line.6. Suppose the numbers of tropical storms in 1998-2002 equal 9, 10, 9, 9, and 10. What happens to the SD of number of tropical storms after adding these five values to the 1950-1997 data? Circle one choice. It increases. It decreases. It doesn’t change. 3Below is a box plot of hurricanes for the three types of El Nino effects.Oneway analysis of number of hurricanes by El Nino effecthurricanes02468101214cold neutral w armel.nino7. Which of the following statements is true?____ The typical deviation from the average for cold El Nino years is larger than the typical deviation from the average for warm El Nino years. ____ The typical deviation from the average for cold El Nino years is smaller than the typical deviation from the average for warm El Nino years. 8. Estimate the percentage of neutral El Nino years with five or more hurricanes. ________9. Estimate the following differences in median number of hurricanes: (median for cold – median for neutral): _________(median for cold – median for warm): _________(median for neutral – median for warm): _________10. True or False: The data suggest that cold El Nino effects are associated with increased hurricane development and that warm El Nino effects are associated with decreased hurricane development. 4Below is a box plot of the relationship between hurricanes and whether West Africa is wet or dry.Oneway Analysis of hurricanes By west.africahurricanes02468101214dry w etw est.africaMeans and Std DeviationsLevel Number Mean Std DevDry 28 5.17857 1.90620Wet 20 6.55000 2.74293Consider these 48 years as a random sample of possible hurricane seasons. There is no apparenttime trend in the data, so this assumption is reasonable. Assume the Central Limit Theorem holdsin each group. 11. (10 points) Researchers theorize that wet years in West Africa have more hurricanes on average than dry years do. Test this claim with a significance test. Report your null and alternativehypotheses, the value of the test statistic, the p-value, and your conclusions. Assume p-values near 0.05 are small.12. (5 points) Is it reasonable to expect the Central Limit Theorem to apply within each group? Explain in no more than four sentences. Below is a scatter plot of number of hurricanes by number of tropical storms5Bivariate Fit of hurricanes By storms02468101214hurricanes5 10 15 20storms13. Estimate the slope and intercept of the regression line: Slope _____ Intercept ______14. Estimate the correlation between number of hurricanes and number of tropical storms: ______15. Estimate the typical deviation of hurricane values around the regression line: ______16. For years in which there are ten tropical storms, estimate the chance that there will be seven or more hurricanes.17. True or False: The data suggest that seasons with high numbers of tropical storms also have high numbers of hurricanes.18. Hot Streaks (5 points per part)6(i) Suppose a baseball player has a 30% chance of getting a hit in any attempt, and that each attempt is independent of other attempts. The player makes four attempts in a game. What is the chance that the player will get at least one hit in a game? (ii) Suppose attempts are not independent. What parts of your calculations in part (i) would not be correct? For your answer, write the exact steps in your calculations that would not be correct.(iii) During the 1978 baseball season, Pete Rose got at least one hit in 44 consecutive games. Assume that, in any attempt, Rose has a 30% chance of getting a hit, and that he makes four attempts per game. Further, assume that each attempt is