MAT209 S05 EXAM I Name_________________________1) 12 points: Jerry has 2 fair coins. He asks if you want to play the following game. Flip both coins, if the coins land HH (2 heads) Jerry will pay you $2 and the game ends. If anything else occurs you get one more chance to flip the coins. If the coins land HH on the second time you flip Jerry will pay you $2, if anything other outcome occurs you get nothing. Jerry says you need to pay $1 to play. Is this a fair game?1b) What is the mean and variance of this game?1c) Jerry told you that Pat played the game and won $2. Given that Pat won $2, what is the probability he got HH the first time he flipped the coins?2) 5 points: What percent of the observations in the standard normal distribution will fall outside the fences on aboxplot, Q1 -1.5*IQR and Q3 + 1.5*IQR ?3) 6 points Your group partner's computer disk died and you lost all the data for your final project. Just before you lost the data, your partner had written down the following information from your final project data. n=10 Mean of y = 30 Variance of y = 144101iiX= 200 1012iiX= 4060The percentage of the variation can be explained by the regression line = .89. Find the regression equation for your data set. 4) 10 points: As a production manager for Pepsi products, you know that the weight of a bottle of diet Pepsi = X ~N(24.2, .15). You have received several customer complaints that people think you are not putting enough Pepsi into each bottle. 5a) 3 points What is the probability that any randomly selected can will weigh less than 24 ounces?4b) 3 points Find a number such that only a 2% of the bottles are getting more Pepsi. In other words find a c such that P(X > c ) = 2%4c) 4 points If you had 15 bottles, what would be the standard deviation of the total of all 15 bottles?[If Xi ~N (24.2, 0.15), What is the standard deviation of T = 121iiX? ]5) 8 points: Here is a shortened version of the summary of a paper in the New England Journal of Medicine that compares the fate of heart attack victims in three types of hospitals. ("Acute myocardial infarction" is medical jargon for a heart attack.) The next four questions concern this summary.Background "America's Best Hospitals," published annually by U.S. News & World Report, assesses the qualityof hospitals. It is not known whether patients admitted to hospitals ranked at the top in cardiology have lower short term mortality from acute myocardial infarction than those admitted to other hospitals.Methods. Using data from the Cooperative Cardiovascular Project on 149,177 elderly Medicare beneficiaries with acute myocardial infarction in 1994 or 1995, we examined the care and outcomes of patients admitted to three types of hospitals: those ranked high in cardiology (top ranked hospitals); hospitals not in the top rank that had onsite facilities for cardiac catheterization, coronary angioplasty, and bypass surgery (similarly equipped hospitals); and the remaining hospitals (non-similarly equipped hospitals). We compared 30-day mortality...Results. Admission to a top ranked hospital was associated with lower adjusted 30-day mortality 5a. The design of this study is A) a completely randomized experiment B) a randomized block experiment C) a multistage national sample survey D) an observational study that compares several treatments 5b. The explanatory and response variables are: 5c. Is the explanatory variable categorical or quantitative?5d. The population about which the study draws conclusions is A) all adult residents of the U.S. B) all heart attack victims C) elderly Medicare beneficiaries who are heart attack victims D) doctors 40 years old or older 6) 6 points 6a. When possible, the best way to establish that an observed association is the result of a cause-and effect relation is by means ofA) the least-squares regression line. B) The correlation coefficientC) A well-designed experiment D) R2 6b. If a sampling method is biased then A) we need to improve the sampling method to remove the bias. B) we need to increase the sample size to remove the bias. C) we should sample from a larger population. D) the sample statistic will be close to the population parameter. 6c. We divide the class into two groups: first year students and others. We then take random samples from eachgroup. This is an example of A) simple random sampling D) stratified random sampling B) clustered sampling E) systematic random sampling C) multistage sampling 7) 4 points An agency of the federal government plans to take an SRS of residents in each state to estimate the proportion of owners of real estate in each state’s population. The populations of the states range from about 494,000 people in Wyoming to more than 34 million in California. Will the variability of the sample proportion vary from state to state if an SRS of size 200 is taken in each state? Explain your answer in the space provided.7b) Will the variability of the sample proportion change from state to state if an SRS of 1/10 of 1% (0.001) of the state’s populations is taken in each state? Explain your answer in the space