(c) x + 4x + 2x + 3x -x+5 (4) x + Sx + 4x + 7 19. Write euch polynomial as a product of irreducible polynomiałs in Q[3).
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Q: Q3: Factorize f (x) = 2x* + x³ + 2x + 4 € Z5[x] as a polynomials product to irreducible over Z5?
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A: Solve the problem as shown below see if they are linear combination of each other and then verify,
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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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- A statistician has to decide on the basis of two obser-vations whether the parameter θ of a binomial distribu-tion is 1 4 or 12 ; his loss (a penalty that is deducted from hisfee) is $160 if he is wrong.(a) Construct a table showing the four possible values ofthe loss function. (b) List the eight possible decision functions and con-struct a table showing all the values of the corresponding risk function.(c) Show that three of the decision functions are notadmissible.(d) Find the decision function that is best according to theminimax criterion.(e) Find the decision function that is best according to theBayes criterion if the probabilities assigned to θ = 14 and θ = 12 are, respectively, 23 and 13 .A research center claims that at least 31% of adults in a certain country think that their taxes will be audited. In a random sample of 800 adults in that country in a recent year, 26% say they are concerned that their taxes will be audited. At α=0.10, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below. (a) Identify the claim and state H0 and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. The percentage of adults in the country who think that their taxes will be audited is not enter your response here%. B. enter your response here% of adults in the country think that their taxes will be audited. C. Less than enter your response here% of adults in the country think that their taxes will be audited. D. At least enter your response here% of adults in the country think…A research center claims that at least 31% of adults in a certain country think that their taxes will be audited. In a random sample of 800 adults in that country in a recent year, 28% say they are concerned that their taxes will be audited. At α=0.10, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below. (a) Identify the claim and state H0 and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. ______% of adults in the country think that their taxes will be audited. B. The percentage of adults in the country who think that their taxes will be audited is not ______%. C. Less than ______% of adults in the country think that their taxes will be audited. D. At least ______% of adults in the country think that their taxes will be audited. (b) Find the critical value(s) and identify the rejection region(s). (c)…
- Kentville, a community of 10,000 people, resides next to a krypton mine, and there is a concern that the emission from the krypton smelter have resulted in adverse effects. Specifically, Kryptonosis seems to have killed 12 of Kentville’s inhabitants last year. A neighboring community, Lanesburg, has 25,000 inhabitants and is far enough from the smelter to not be affected by the emission. In Lanesburg, only three people last year died of Kryptonosis. Given that the number of deaths in Kentville and their causes last year were: Heart attack=7 Accidents=4 Kryptonosis=12 Other=6 What is the risk of dying of Kryptonosis in Kentville relative to non-contaminated locality?What is the risk of dying of Kryptonosis in Kentville relative to deaths due to other causes? How many times the chance of dying of Kryptonosis compared to dying of accidents ? How many times the chance of dying of Kryptonosis compared to Other causes?The Stanford University Heart Transplant Study was conducted to determine whether an experimental heart transplant program increased lifespan. Each patient entering the program was designated an official heart transplant candidate, meaning that he was gravely ill and would most likely benefit from a new heart. Patients in the treatment group got a transplant and those in the control group did not. Of the 34 patients in the control group, 4 were alive at the end of the study. Of the 69 patients in the treatment group, 24 were alive. The contingency table below summarizes these results.A research center claims that at least 28% of adults in a certain country think that their taxes will be audited. In a random sample of1000 adults in that country in a recent year, 23%say they are concerned that their taxes will be audited. At α=0.10, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below. (a) Identify the claim and state H0 and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. nothing% of adults in the country think that their taxes will be audited. B. Less than nothing% of adults in the country think that their taxes will be audited. C. At least nothing% of adults in the country think that their taxes will be audited. D. The percentage of adults in the country who think that their taxes will be audited is not nothing%. Let p be the population proportion of…
- The PR team at Bruno conducts their hiring process in two stages. For applicants who are classified as A, B, and G in the first stage, the chances of getting hired full-time after the second stage are 74%, 43% and 26% respectively. If an applicant is not hired full-time, they are either put on a probation list, or rejected. Unselected applicants of all categories (A, B, and G) are half as likely to be put on the probation list as being rejected. During the first stage of the most recent hiring, 22% of the applicants were rated A, 39% were rated B, and the rest were rated G. If a randomly chosen applicant was rejected by three out of eight individual interviewers, what is the probability that they were rated A?An insurance company offers four different deductible levels—none, low, medium, and high—for its homeowner’s policyholders and three different levels—low, medium, and high—for its automobile policyholders. The accompanying table gives proportions for the various categories of policyholders who have both types of insurance. For example, theproportion of individuals with both low homeowner’s deductible and low auto deductible is .06 (6% of all such individuals).Suppose an individual having both types of policies is randomly selected.a. What is the probability that the individual has a medium auto deductible and a high homeowner’s deductible?b. What is the probability that the individual has a low auto deductible? A low homeowner’s deductible?c. What is the probability that the individual is in the same category for both auto and homeowner’s deductibles?d. Based on your answer in part (c), what is the probability that the two categories are different?e. What is the probability that the…If a study determines the difference in average salary for subpopulations of people with blue eyes and people with brown eyes is NOT significant, then the populations of blue-eyed people and brown-eyed people are ________ different salaries. a) unlikely to have b) very unlikely to have c) guaranteed to have d) guaranteed to not have
- A medical researcher says that less than 74%of adults in a certain country think that healthy children should be required to be vaccinated. In a random sample of 600adults in that country, 71% think that healthy children should be required to be vaccinated. At α=0.01, is there enough evidence to support the researcher's claim? Complete parts (a) through (e) below. (a) Identify the claim and state H0 andHa. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) Fill the percentage on the correct answer A. % of adults in the country think that healthy children should be required to be vaccinated. B. Less than %of adults in the country think that healthy children should be required to be vaccinated. C. The percentage of adults in the country who think that healthy children should be required to be vaccinated is not %. D. More than…A newly appointed school district superintendent releases a plan for thenext 20 years that affects the schools within the boundaries of the district.In this plan, there is new policy that states that if a high school has lessthan 100 students, then the school will be shut down. Calamanco HighSchool has a population of 1,417 students, but it is losing students at anaverage rate of 109 students per year. This school used to house morethan 5,000 students but the district has been struggling in recent years andlosing people to more affluent nearby districts and cities. Somecommunities are concerned about this decreasing rate because therewill be a time when the district may shut the school down. Let xx representthe number of full years that the school is operational.Part A: If this trend continues, write a function that gives the studentpopulation at Calamanco High School after xx years before theschool is shut down by the district. Part B: What constraints does this situation put on the…The television show Lett3rs has been successful for many years. That show recently had a share of 19, which means, that among the TV sets in use, 19% were tuned to Lett3rs. An advertiser wants to verify that 19% share value by conducting its own survey, and a pilot survey begins with 10 households have TV sets in use at the time of a Lett3rs broadcast. If at most one household is tuned to Lett3rs, does it appear that the 19% share value is wrong? (Hint: Is the occurrence of at most one household tuned to Lett3rs unusual?) A. no, it is not wrongB. yes, it is wrong