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- 38. Prove or disprove that .11. (See Exercise 10.) According to Definition 5.29, is defined in by if and only if . Show that if and only if . 10. An ordered field is an ordered integral domain that is also a field. In the quotient field of an ordered integral domain define by . Prove that is a set of positive elements for and hence, that is an ordered field. Definition 5.29 Greater than Let be an ordered integral domain with as the set of positive elements. The relation greater than, denoted by is defined on elements and of by if and only if . The symbol is read “greater than.” Similarly, is read “less than.” We define if and only if. As direct consequences of the definition, we have if and only if and if and only if . The three properties of in definition 5.28 translate at once into the following properties of in . If and then . If and then . For each one and only one of the following statements is true: . The other basic properties of are stated in the next theorem. We prove the first two and leave the proofs of the others as exercises.Figures obtained from a city's police department seem to indicate that of all motor vehicles reported as stolen, 63% were stolen by professionals (P), whereas 37% were stolen by amateurs (primarily for joy rides) (A). Of the vehicles presumed stolen by professionals, 25% were recovered within 48 hours (R<48), 23% were recovered after 48 hours (R>48), and 52% were never recovered (N). Of the vehicles presumed stolen by amateurs, 33% were recovered within 48 hours, 63% were recovered after 48 hours, and 4% were never recovered. (b) What is the probability that a vehicle stolen by a professional in this city will be recovered within 48 hours?(c) What is the probability that a vehicle stolen in this city will never be recovered? (Round your answer to four decimal places.)
- In a recent study, 50males used a new weight-loss supplement, and 38 of them experienced weight loss after two weeks. In the same study, 20 females used the same supplement, and 16of them experienced weight loss after two weeks.Fill in t he blanks below to make the most reasonable statement possible. The new weight-loss supplement was less effective on ▼(Choose one: males/females) in the study. That is because only ____% of them lost weight after two weeks, whereas ____% of the ▼(Choose one:males/females) lost weight after two weeks.How should I choose between d and e- if d does not exist neither would e, right?E. Show that both ℝ and ℝ2 may be covered by countably many open balls.
- Of the high blood pressure patients in a particular clinic, 62% are treated with medicationX, the remainder with medication Y. No patient is given both medications. It is known that 1.4% of thepatients using medication X suffer from fainting episodes, as do 2.9% of the patients using medicationY. A patient known by the clinic to have high blood pressure suffers a fainting episode, but she doesnot know which medication she is on. Which medication is she most likely taking?If θ̂ is a point estimator of θ, prove that MSE(θ̂) = V(θ̂) + (B(θ̂))2At a certain school 60 of the 100 boys and 60 of the 80 girls signed up for the senior trip. Is there an associa-tion between going on the trip and gender? A) We can’t tell, because the class doesn’t have the samenumber of boys and girls.B) Yes, because the same number of boys and girlssigned up.C) Yes, because a lower percentage of boys signed upthan of girls.D) No, because the people on the trip were 50% boysand 50% girls.E) No, because the sign-up rate was higher among girlsthan among boys.
- AT&T was running commercials in 1990 aimed at luring back customers whohad switched to one of the other long-distance phone service providers. One suchcommercial shows a businessman trying to reach Phoenix and mistakenly gettingFiji, where a half-naked native on a beach responds incomprehensibly in Polynesian.When asked about this advertisement, AT&T admitted that the portrayed incidentdid not actually take place but added that this was an enactment of something that“could happen.”12 Suppose that one in 200 long-distance telephone calls is misdirected. What is the probability that at least one in five attempted telephone calls reachesthe wrong number? (Assume independence of attempts.)Refer to the information in the previous problem. Given that your longdistance telephone call is misdirected, there is a 2% chance that you will reach a foreign country (such as Fiji). Suppose that I am now going to dial a single long-distancenumber. What is the probability that I will erroneously…show that if A occurs in a larger proportion of the cases where B is than wgere B is not, then B will occur in a larger proportion of cases where A is than where A is not.if H0 is u equal to 21, H1 is u is greater than 21, then the hypothesis is Oa Two tailed b. One talled and left tailed c.One laled and right tailed Od Incorrect hypothesis