Actual Problem: Sherlock Holmes is called in to investigate a missing document from themayor's office. A look at her meeting calendar suggests that she meets with a local politician15% of the time, her business partner 30% of the time, her assistant 50% of the time, and alocal citizen 5% of the time. Sherlock Holmes conducts some interviews and estimates thatwhenever they meet:• there is a 5% chance the politician steals the document;• there is a 3% chance the business partner wants the document;• there is a 1% chance that the assistant misplaces the document;• there is a 5% chance that the local citizen accidentally takes the document.Who is most likely to have caused the missing document? Hint: define the events S{document is missing}, E;each person i and then we need to find the person who has the largest conditional probability.Hint: you'll need to use Baye's rule.%3D{meeting was with person i}. We are looking for P(E;|S) for||

Answered: Actual Problem: Sherlock Holmes is…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Suppose I flip a fair coin n = 20 times. A psychic tries to predict the outcome before each flip. Three researchers have different ideas about the psychic's ability. There is Sydney, the Skeptic (S), who thinks the psychic's success rate is between 49% and 51%. There is Morgan, the Mark, M, who thinks that the psychic's success rate is 80%. And there is Carter, the Cynic (C), who thinks the psychic's success rate is 10%. Specifically: S+ 0 ~ U(.49, .51) M + 0 = .80 C0 = .10 %3D In all cases, assume the number of successful predictions follows a binomial distribution with success rate 0. Usek for the number of successes and n for the number of trials. Given all that: Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Carter over Morgan. Call that Bayes factor Bc:M Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Morgan over Sydney. Call that Bayes factor BM:S Determine the formula for the Bayes factor (a.k.a., likelihood…
In a study carried out among low-income families in the young towns of Detroit, it was found that 30% spent less than $8 weekly on purchasing charcoal and consumed products from soup kitchens. 35% spent $8 to $15 weekly on the purchase of charcoal. 5% spent more than $15 weekly on the purchase of charcoal and consumed products from the soup kitchen. 15% spent more than $15 each week buying coal. Finally, 55% did not consume the products of the soup kitchens.If you randomly choose a low-income familyto. What is the probability that you spend less than $8 weekly on purchasing coal?b. What is the probability that you do not consume the products of the soup kitchens and spend 8 to 15 dollars buying charcoal?C. If the family spends more than $15 weekly on purchasing charcoal, what is the probability that they will not consume the products from the soup kitchens?d. If the family does not consume products from soup kitchens, what is the probability that it will spend less than 8 soles per…
Suppose you try to conduct a presidential approval poll of 10,000 likely U.S. voters. You know that 44% of the voters are registered with the Independent party, 28% are registered with the Reform party and 23% are registered with the Green party. If you are going to construct a representative sample of this population, approximately how many of the likely voters in the sample should be Green party?
Example 1: The owner of a local restaurant chain in town was trying to determine the best location to open her next restaurant and she had narrowed it down to two locations. She wanted to make her decision based on how interested residents in each area were in her restaurant. So she hired an independent company to survey residents from each neighborhood to gauge their interest. In the first neighborhood, 120 residents were surveyed and 84 of them expressed interest in the new restaurant. In the second neighborhood, 200 residents were surveyed and 110 of them expressed interest in the new restaurant. Carry out an appropriate hypothesis test at the a = 0.02 level to determine if there is sufficient evidence to suggest that one neighborhood is more interested in the new restaurant than the other.
A construction company submitted a bid for a large, public construction project. The company’s management initially felt they had a 50-50 chance of getting the project. However, the department to which the bid was submitted subsequently requested additional information on the bid submitted by this company. Past experience indicates that for 75% of the successful bids but only for 40% of the unsuccessful bids the agency requested such additional information. Question: Given that the construction company was asked for additional information, what is the probability that it will get the project?
Many states mandate tests that have to be passed in order for the students to graduate with a high school diploma. A local school superintendent believes that after-school tutoring will improve the scores of students in his district on the state's graduation test. As a trial run, a tutor agrees to work with 15 students for a month. The superintendent ask the school board to implement this after-school tutoring program if there is evidence that student scores would increase by an average of more than 20 points. Create a 95% confident level to estimate the true score increase. 25.4 23.3 17.8 21.3 14.8 28.8 22.5 23.6 32.3 15.4 23.4 27.5 18.8 19.1 20.4 a. Confidence Interval b. Conclusion
At LLD Records, some of the market research of college students is done during promotions on college campuses, while other market research of college students is done through anonymous mail, phone, internet, and record store questionnaires. In all cases, the company solicits an "intent-to-purchase" score from the student, with 0 being the lowest score ("no intent to purchase") and 100 being the highest score ("full intent to purchase"). The manager finds the following information for 150 intent-to-purchase scores for a soon-to-be-released CD: Sample Sample Sample size Group mean variance On campus 30 64.5 68.9 By mail 30 63.0 77.1 By phone 30 62.8 125.1 By internet 30 62.3 106.0 In a store 30 68.2 85.9 Send data to calculator Send data to Excel Suppose that the five populations of scores from which these samples were drawn are approximately normally distributed and have the same mean and the same variance. Answer the following, carrying your intermediate computations to at least three…
In a US presidential election, the incumbent president wins with 51.5% of the vote to 48.2% for the primary challenger (and .3% to others). In a nationwide telephone poll of 1000 people conducted exactly one week before the election by a university polling group, 49% of people polled supported the incumbent president, 50% supported the challenger, and 1% supported other candidates. a. For the polling study, what was the population of interest? b. What was the sample? c. Why did the sample results differ from the population? d. What are two constants that might have limited the generalizability of the polling results?
A research wants to determine if pre-natal exposure to the hormones in birth control pills alters the sex makeup of midshipman fish populations (which are typically half male and half female).Specifically, the researcher wishes to test the hypothesis that exposure to hormones will increase the number of females in the population.The researcher exposes a group of pregnant midshipman fish to birth control hormones and records the sex of the first 13 offspring birthed.They then observe that 11 are female.Use a sign test and a alpha of .05 to test the indicated hypothesis.What is the critical value?
Cable TV choices: A telecommunications company provided its cable TV subscribers with free access to a new sports channel for a period of 1 month. It then chose a sample of 404 television viewers and asked them whether they would be willing to pay an extra $10 per month to continue to access the channel. A total of 35 of the 404 replied that they would be willing to pay. The marketing director of the company claims that the percentage of all of its subscribers who would pay for the channel differs from 6%. Can you conclude that the director's claim is true? Use the a=0.10 level of significance and the P-value method with the table. Part: 0 / 4 Part 1 of 4 (a) State the appropriate null and alternate hypotheses. Ho : H₁ : This hypothesis test is a (Choose one) ▼ test. Part: 1 / 4 Part 2 of 4 P-value= Part: 2 / 4 Part 3 of 4 (b) Compute the P-value. Round the answer to at least four decimal places. (c) Determine whether to reject Ho. (Choose one) Part: 3 / 4 Part 4 of 4 X (d) State a…
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In a series of studies, Sebastian Deri and his colleagues (2017) asked multiple groups about the number of friend groups they had and how often they attended different social events. They then asked participants how they thought their own numbers compared to other people's: Did participants see themselves as less social, the same as, or more social than others? In the first study, the researchers reported that: "Three hundred four participants from Amazon's Mechanical Turk (150 women; Mage = 37.1; 78% White, 10% Black, and 6% Asian) completed a survey in exchange for modest payment" (p. 860). What do the researchers mean by "Amazon's Mechanical Turk" with respect to their sample of participants? O A. An archival data set that already exists and from which researchers can use data O B. An online tool that researchers can use to recruit people to participate in research in exchange for a small payment O C. An e-book sold by Amazon that includes contact information for possible…

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