4. (Sets) In a survey of 400 people about COVID-19 vaccination, the following informationwas obtained.• Some people had all their doses (first, second, and booster) with the same type ofvaccine, while others received different types of vaccines.• 31 people had three types of vaccine (Pizer, AstraZeneca, and Moderna).91 people had both Pfizer and Astrazeneca.50 people had AstraZeneca and Moderna.• 46 people had Moderna and Pfizer.• 212 had Pfizer.• 164 had AstraZeneea.• 105 had Moderna.Using the abbreviation P, AZ, and M for the three vaccines, please answer:(a) How many people had both Moderna and Pfizer, but not AstraZeneca?(b) How many people in the set AZ nPOM?(c) How many people had more than one type of vaccine?(d) How many people only received the Pfizer vaccine?(e) How many people received none of the three types of vaccine?

Given are three types of vaccine information which is obtained after surveying 400 people. First we…

Answered: 4. (Sets) In a survey of 400 people…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The raw data gathered on a university campus from a survey of art degree majors and their residency status were as follows: α11 =67, a12 = 33, a13 = 22, a21 = 132, α22 = 78, a23 = 39, α31 = 31, a32 = 11, α33 = 4, α41 = 74, a42=75, a43 = 22 The following contingency table was created based on the above data, where you will need to calculate the grand total, the total for each row, and the total for each column on your own before answering the question that appears after the table. Digital Media Drawing/Painting Sculpture Studio Arts Total In-State Students 67 132 31 74 Out-of-State Students 33 78 11 75 International Students 22 39 22 Total Calculate the probability that someone is a studio arts major AND an In-State student. (For answers up to four decimal places, enter the number in the box below without rounding it. For answers that have more than four decimal values, round your answer to four decimal places).
AD (Alzheimer's disease) causes progressive cognitive impairment. A diagnostic blood test for AD was proposed. An evaluation of the blood text involved fifty known AD patients and forty control who did not have AD. Of those who had AD, forty eight tested positive on the blood test and two tested negative. Of those without AD, three tested positive on the blood test and thirty seven tested negative. a. Complete the table below:
A pharmaceutical company proposed a vaccine that would combat paralytic polio. Two independent random samples were collected from the population. One random sample of 201,229 was given the placebo, and among them 100,910 contracted paralytic polio. The other random sample of 200,745 was given the vaccine, and among them 50,033 people ended up contracting paralytic polio. Let the true proportion of cases of paralytic polio given placebo be p1p1 and the true proportion of cases of paralytic polio given vaccine be p2. Calculate the upper bound of a 95% confidence interval for p1−p2. Round your answer to three decimal places.
A psychologist wants to know whether viewing more violent TV shows affects aggressive behavior. 12 children were chosen at random for an experiment and randomly allocated to one of two conditions. In condition 1, six kids were given an aggressive behavior test. The more aggressive the conduct, the higher the score. In condition 2, six children were given the identical test after watching two hours of tv shows. The following results were obtained. Condition 1 5 14 6 8 7 6 Condition 2 12 14 14 8 15 9 Assume the obtained value of the appropriate statistic is t obt = -2.431, using α = 0.05, 2 tail, and t crit = +2.228 and -2.228, what do you conclude? a. retain null hypothesis, suggesting that violent TV show does not affect aggression. b. reject null hypothesis, suggesting that violent TV show affects aggression.
Suppose that Mairin has knit a collection of wool‑blend infinity scarves that she wants to sell in her Etsy shop for $28.00 each. However, she is worried that if the average price of comparable scarves is less than $28.00, hers would be less likely to sell. Mairin selected a random sample of 9 similar hand‑knit, wool‑blend infinity scarves, and their prices are as follows. $21.75,$24.00,$27.25,$29.95,$23.00,$26.00,$27.80,$33.50,$27.00$21.75,$24.00,$27.25,$29.95,$23.00,$26.00,$27.80,$33.50,$27.00 Use a left‑tailed one‑sample ?t‑test to determine whether the average price of hand‑knit, wool‑blend infinity scarves sold on Etsy is less than $28.00. Assume that the prices of all comparable scarves are normally distributed. Mairin should (reject, accept, fail to accept) her null hypothesis. There is (sufficient, no, insufficient) evidence that the mean price of hand‑knit, wool‑blend infinity scarves is (greater than, different from, less than, equal two) $28.00.
Angioplasty is a medical procedure in which an obstructed blood vessel is widened. In some cases, a wire mesh tube, called a stent, is placed in the vessel to help it remain open. A study was conducted to compare the effectiveness of a bare metal stent with one that has been coated with a drug designed to prevent reblocking of the vessel. A total of 5319 patients received bare metal stents, and of these, 848 needed treatment for reblocking within a year. A total of 1122 received drug-coated stents, and 142 of them required treatment within a year. Can you conclude that the proportion of patients who needed retreatment differs between those who received bare metal stents and those who received drug-coated stents? Let p1 denote the proportion of patients with bare metal stents who needed retreatment and p2 denote the proportion of patients with drug-coated stents who needed retreatment. Use the =α0.10 level of significance and the P -value method with the…
To investigate the effect of price on toaster sales, a chain of department stores decided to raise the price of a certain brand of toaster in 20 randomly selected stores (Sample A) and to lower the price in 10 randomly selected stores (Sample B). Monthly revenue (number sales x sales price) from these toasters was recorded for each of the 30 stores. Results from the two samples are as follows: No. of stores Мean Std. Dev. Sample A Sample B $842 $817 $217 $202 20 10 If you considered these to be independent samples, what would be the pooled estimate of the standard deviation for revenue? Calculate a 95% confidence interval for the difference between (а) (b) the two means.
A psychologist wants to know whether viewing more violent TV shows affects aggressive behavior. 12 children were chosen at random for an experiment and randomly allocated to one of two conditions. In condition 1, six kids were given an aggressive behavior test. The more aggressive the conduct, the higher the score. In condition 2, six children were given the identical test after watching two hours of tv shows. The following results were obtained. Condition 1 5 14 6 8 7 6 Condition 2 12 14 14 8 15 9 Q1, The alternative (H1) hypothesis and null (H0) hypothesis are (2-tail) _________. a. H1: violent TV show does not affects aggressive behavior H0: violent TV show affects aggressive behavior b. H1: violent TV show affects aggressive behavior H0: violent TV show does not affect aggressive behavior
A market research group is interested in estimating the market share of three airline companies, A, B and C, operating on a particular flight path. These three airlines are the only companies operating on this route. Airline B claim that they have 50% of the business with the remaining percentage shared equally amongst airlines A and C, i.e. 25% each. The market research group decide to carry out an independent study and question a random sample of 97 people visiting an airport on a particular day. Each person was given price, timetables and service details of flights on this route for each of the three airlines. Provided with this information they were asked to select their airline of choice.The survey revealed the following observed frequencies Airline A - 26 Aurline B - 49 Airline C - 22 Test if there is any evidence to suggest that the airline's claim is incorrect, at significance level α = 0.05. Complete the test by answering the following questions : Which of the following is the…
To study the effectiveness of possible treatments for insomnia, a sleep researcher conducted a study in which four participants were instructed to count sheep (the Sheep Condition), four were told to concentrate on their breathing (the Breathing Condition), and four were not given any special instructions. The average number of minutes taken for each participant to fall asleep over the next seven days were 14, 28, 27, and 31 minutes for the Sheep condition; 25, 22, 17, and 14 minutes for those in the Breathing condition; and 45, 33, 30, and 41 for the Control condition. Using the .05 significance level, did the different techniques have different effects? What is the null hypothesis? What is the research hypothesis?
The ability of lizards to recognize their predators via tongue flicks can often mean life or death for lizards. Seventeen juvenile common lizards were exposed to the chemical cues of the viper snake. Their responses, in number of tongue flicks per 20 minutes, are presented below. 319, 676, 710, 455, 744, 200, 370, 200, 472, 336, 455, 642, 795, 795, 438, 540, 489 Assuming normal distribution, a) Find a 90% confidence interval for the mean number of tongue flicks per 20 minutes for all juvenile common lizards. Assume a population standard deviation of 190.0. Note: The sum of the data is 8636. Confidence interval: (, ). b) Which of the following is the correct interpretation for your answer in part (a)? A. We can be 90% confident that the mean number of tongue flicks per 20 minutes for this sample of 17 lizards lies in the interval B. There is a 90% chance that the mean number of tongue flicks per 20 minutes for all juvenile common lizards lies in the interval C. We can be 90% confident…

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