Give a detailed work please thankyou

7. Knowledge of economics is divided into 3 groups: 20% of the population is Excellent, 60% Good, and 20% Weak. Past studies have found that 70% of those in the Excellent group give the correct answer to a certain question, as do 50 percent of those in the Good group and 30% of those in the Weak group. If a person gives a correct answer to this question, what is the probability that this person is in the Excellent group? 8. Why do you suppose that the time it takes for bags of microwave popcorn to be fully popped is (approximately) normally distributed, but the time is takes students to answer 10 math problems is not? 9. Three prisoners, A, B and C, are in separate cells and sentenced to death. The governor has randomly selected one of them to be pardoned. The warden knows which one, but is not allowed to tell. Prisoner A begs the warden to let him know the identity of one of the others who will be executed. "If B is to be pardoned, give me C's name. If C is to be pardoned, give me B's name, And if I'm to be pardoned, flip a coin to decide whether to name B or C." The warden tells A that B is to be executed. Prisoner A is pleased because he believes that his probability of surviving has gone up from 1/3 to 1/2, as it is now between him and C. Prisoner A tells C the news, who is also pleased, because he reasons that A still has a 1/3 chance of being pardoned, so his chance has gone up to 2/3. What is the correct answer? 10. While a baseball pitcher was making warmup throws before a game, his coach said, "Stop throwing good pitches; you need to get your bad pitches out of the way." What do you think?5. Assume that, taking point spreads into account, a person who bets on a football game has a 50% chance of winning the bet, and that the outcome of any game does not depend on the outcomes of other games. Most betting cards work as follows: the bettor picks the winners of n games and is paid a specified amount if he or she wins all n games. For example, for a bet of x dollars, you can purchase any one of the following three cards and be paid the indicated amounts: 1. 6x for correctly picking 3 out of 3 games. b. 11x for correctly picking 4 out of 4 games. c. 16x for correctly picking 5 out of 5 games. What is the expected value of the net return from each of these bets? What does this structure of expected values suggest about bettor preferences? 6. An American roulette wheel has 38 pockets, an equal number of red and black pockets numbered 1 to 36, and two green pockets (0 and 00). The wheel is spun one direction and the ball is spun the opposite direction until the ball loses momentum and drops into one of the pockets-which is then the winning number. Assume that the game is fair with every pocket equally likely and every outcome independent. 28 9 263921 7 203217 5 22341 6014 3415 3 243613 1 60 23351 a. What is the probability that the numbers 1, 2, and 3 will be the winning numbers, in that order, on the next three spins? b. What is the probability that 23 will be the winning number at least once in the next 10 spins? c. What is the probability that a green number (either 0 or 00) will be the winning number on all five of the next 5 spins? d. What is the expected wait until a green number is the winning number?1. In 2015, a widely circulated news story was titled, "Selfies have killed more people than sharks this year." The subtitle was "Humans: still the world's deadliest predator." The story backed up its claim that humans are the deadliest predator with a report of 8 deaths from shark attacks in 2015 compared to 12 deaths related to taking ill-advised selfies, including people falling off cliffs, crashing their cars, being hit by trains, and shooting themselves while posing with guns. The story concluded, that "not only does the likelihood of being killed by a shark pale in comparison to the deadliness of selfies, it's also a lot lower than the number of deaths caused by dog attacks and home renovations. In fact, pretty much everything you do today (particularly if it involves a car) is more likely to kill you than a shark." Why is this report misleading? 2. In the card game War, a standard deck of 52 playing cards is divided evenly between two players. Each player turns over a card, and the player with the higher card wins both cards and puts them at the bottom of his or her deck. (Aces are high, then kings, queens, and so on; the suit does not matter.) The game continues until one player runs out of cards. If the two cards turned over are the same rank (for example, two 7s or two jacks), it is War. Each player then plays one card face down and one card face up, and the higher face-up card wins all 6 cards. What is the probability that the very first play of the game will be War? 3. "A 2001 report by Harvard University's College Alcohol Study compared colleges that ban all alcohol to those that do not, finding that students at colleges with a ban were 30% less likely to be heavy episodic drinkers and more likely to abstain from alcohol." What problem do you see interpreting this study? 4. A seemingly healthy woman has a physical checkup which involves a battery of tests of 20 risk factors (such as cholesterol) that might indicate a health problem. For each test, the result is flagged as abnormal if the reading is unusually high or low-specifically, if it outside a range that encompasses 95% of the readings for healthy women. Thus, if a woman is healthy, there is only a 5% chance that her reading on a test will be outside the normal range. Assuming that the test results are independent, what is the probability that a healthy woman who takes 20 such tests will have two or more abnormal readings?16. A researcher used 2011 data for 30 developing countries to estimate a model of real per capita GDP, in U.S. dollars. The education variables are the percent of people of the appropriate age enrolled in school; for example, the total number of females enrolled in primary schools divided by the number of females of primary school age. The adolescent fertility rate is births per 1,000 women ages 15-19. The researcher initially estimated Model 1. After noting the high multicollinearity among the explanatory variables, the researcher estimated Model 2. Model 1 Model 2 Coefficient t-value Coefficient t-value Intercept 92,229 1.17 16,380 0.72 Female primary education 1,154 0.64 726 1.53 Male primary education -2,219 0.96 -899 1.68 Female secondary education -1,771 1.57 -1,081 2.21 Male secondary education 1,901 1.80 1,113 2.16 Female tertiary education 265 0.47 263 0.71 Male tertiary education -84 0.10 192 0.37 Volume of exports 429 0.11 Unemployment rate -290 0.17 Adolescent fertility rate -89 0.43 R-squared 0.804 0.684 The author concluded that, "The R-squared value decreased from 0.804 to 0.684. However, this model provides more precise estimates of the coefficients of the explanatory variables. The standard errors fall by almost half and the t-values for almost all variables, specifically secondary education for both genders, are statistically significant, unlike in the previous model." What do you think? 17. A study of CO2 emissions estimated this model using 2010 data for 161 countries: Y =-807,815 + 14,370X1 + 3,655X2 + 9,134X3 where Y = CO2 emissions (kilotons), X1 = industrial percentage of GDP, X2 = agricultural percentage of GDP, and X3 = services percentage of GDP, with X1 + X2 + X3 = 100. The author reported that, The standard errors were quite large: 16,418,125 for Y, 163,877 for XI, 164,871 for X2, and 164,305 for X3. The I value for Y was 0.0492, and its p value was 0.4804. XI had a t value of 0.0877 and a p value of 0.4652 while X2 had a t value of 0.0222 and a p value of 0.4912 and, finally, X3 had a t value of 0.0556 and a p value of 0.4779. a. What problems do you see with this model specification? b. How would you respecify the model? b. What problems do you see with the reported results?12. Explain why the proposed test is wrong and identify the correct test: I used a chi-square test to look at the relationship between high school graduation rates in California counties and the per capita income in the past 12 months in these counties. Here are my results for the first four counties alphabetically in California: Alameda Alpine Amador Butte Graduation rate 86 91 88 87 Per capita income $35,434 27,135 26,969 23,556 Graduation rate is is the percent of persons age 25+ who graduated from high school and per capita income is annual income (in 2012 dollars) for the years 2008 through 2012, The chi-squared value is 8.58 and the p-value is 0.0353, which means we would reject the null at the 5% level, but not the 1% level. 13. A scientist visited the homes of Denver children who had died of cancer and found that many lived near power lines. A Swedish study analyzed data on cancer deaths and exposure to electro-magnetic fields (EMFs) from power lines. They did nearly 800 statistical tests and found that children diagnosed with leukemia had above-average exposure to EMFs. What statistical problems do you see with these two studies? Be specific. 14. A classic test lets a monkey choose M&Ms until the researcher identifies three colors (say blue, red, and green) that the monkey seems to prefer about equally. The monkey is then offered a choice between two M&M's-say, blue and red. If the monkey chooses blue, then the monkey is offered a choice between red and green. Two-thirds of the time, the monkey chooses green, apparently confirming the theory of choice rationalization: after we reject something, we devalue it. Now suppose that the monkey is not perfectly indifferent between blue, red, and green M&Ms, but in fact prefers blue to red. What is the probability that the monkey also prefers green to red? (Assume that the monkey is randomly chosen from a group of monkeys that are equally likely to prefer one color to another.) 15. Data on the profits (return on assets) of 100 firms were grouped into quartiles based on their 1930 profits: the top 25, second 25, third 25, and bottom 25. The average profits in 1930 and 1920 were then calculated for the firms in these 1930 quartiles. How would you explain the graph? Profit, % 50 7 30- 20- 10- 1920 19306. Suppose that the damage award favored by individual potential jurors in a particular personal injury case can be described by a normal distribution with a mean of $5,000,000 and a standard deviation of $2,000,000. (This probability distribution is across randomly selected jurors.) What percentage of potential jurors favor an award of more than $5,500,000? 7. Continuing the preceding exercise, assume that a jury is a random sample from this distribution and that the jury's damage award is the average of the awards favored by the individual jurors. Carefully explain the differences in the awards that can be anticipated with a 6-person jury versus a 12-person jury. 8. A medical study reported that Treatment A was more successful than Treatment B in treating small kidney stones (90% versus 80%) and in treating large kidney stones (70% versus 60%) but, overall, combining the data for large and small kidney stones, Treatment B was more successful. Is this possible or did they make a mistake? Explain your reasoning and use a numerical example to illustrate your argument. Be specific. 9. In the traditional game Tong, two players, E and O, simultaneously reveal a hand showing one, two, or three fingers. If the sum of the fingers on the two players' hands is even, O pays $1 to E. If the sum is odd, E pays $1 to O. If each player is equally likely to show one, two, or three fingers and their choices are made independently, what is the expected value of this game for E? For O? 10. Explain why the proposed test is wrong and identify the correct test: I will ask students from all five of the undergraduate Claremont Colleges: "Do you think your intelligence is above or below average compared to other students of your gender at your college? " I will analyze the data using an ANOVA F-test to test the null hypothesis that students are equally likely to answer above or below average, regardless of college or gender. 11. Explain why the proposed test is wrong and identify the correct test: My question is "Does playing on home ice in the National Hockey League (NHL) give the home team a better chance to win? " I will choose six NHL teams and, for each team, use a Z single-sample categorical test of the null hypothesis that the chance of winning at home is equal to one half.1. An Internet company's CEO gave her Board of Directors a graph prepared by the company's finance group that showed the company's revenue over the previous seven quarters. The Board grilled the CEO, asking her to explain why revenue was down so much. How would you have responded? Revenue 1,060,000- 1,050,000- 1,040,000- 1,030,000- 1,020,000- 1,010,000- 1,000,000- 2009 2010 2011 2. If you are dealt 5 cards from a standard 52-card deck, what is the probability that 4 of the 5 cards will be aces? 3. The Pizza Principle says that in New York City since the 1960s, the cost of a subway ride has been roughly equal to the cost of a slice of pizza. How, as a statistician, would you explain this relationship? 4. The equation y = a + Bx + &, where y = unemployment and x = production, was estimated using monthly 2013 data, entering the months in a computer program in order: January, February, March, and so on. How would the estimates be affected if we enter the data backwards: December, November, October, and so on? 5. Nate Silver's book The Signal and the Noise looks at five mortgages, each of which has a 5% chance of defaulting. Assuming independence, he calculates that probability that at least one will default as (5 0.05095' =0204 What is the correct probability