A grocery supplier has two potato fields, A and B, growing the same kind of potato. Howeverthe field A produces potato with proportion of 0=8% of potatoes that are rotten inside, whilefield B produces 0=6% of rotten potatoes. The grocery manager asked the supplier to deliverpotato from field A. The delivery arrived. The manager is bayesian and based on her priorexperience with the supplier, she believes that the probability of the delivery being from fieldA (i.e. that the supplier is honest) is 40%. While the supplier hasn't left yet, the managerquickly checks 20 potatoes and discovers x = 4 of them to be rotten.Find the posterior probability P(0 = 0.08 | x = 4) that the potato comes from the field A,after finding 4 rotten potatoes in the sample.0.8980.158O 0.277O 0.599

Using Bayes theorem, we can find the posterior probability that the potatoes come from field A,…

Answered: A grocery supplier has two potato…

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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A new vaccine against the coronavirus has been developed. The vaccine was tested on 10,000 volunteers and the study has shown that 65% of those tested do not get sick from the coronavirus. Unfortunately, the vaccine has side effects and in the study it was shown that the probability of getting side effects among those who did not get sick is 0.31, while the probability of getting side effects among those who got sick from corona despite vaccination is 0.15. (a) Draw an event tree and show on the event tree all the probabilities in branch points.
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A new screening test for Lyme disease is developed for use in the general population. The sensitivity and specificity of the new test are 60% and 70%, respectively. Five hundred people are screened at a clinic during the first year the new test is implemented. Assume the true prevalence of Lyme disease among clinic attendees is 10%. Calculate the predictive value of a positive test.
Determine whether the results appear to have statistical significance, and also determine whether the results appear to have practical significance. In a study of a birth sex selection method used to increase the likelihood of a baby being born female, 1916 users of the method gave birth to 941 males and 975 females. There is about a 23% chance of getting that many babies born female if the method had no effect. Because there is a 23% chance of getting that many babies born female if the method had no effect, the method couples would likely use a procedure that raises the likelihood of a baby born female from the approximately 50% rate expected by chance to the % produced by this method. (Round to the nearest integer as needed.) So, this method has statistical significance. does not have practical significance. should be used to make conclusions. has practical significance.
In a randomized clinical trial, 888 people were placed given Drug A and 930 were given Drug B. The researcher's goals were to determine which drug had better efficacy against T.B. Of those who were given Drug A, 300 contracted T.B. Of the subjects who were given Drug B, 500 contracted T.B. Calculate and interpret the risk ratio of Drug B compared to Drug A for getting T.B.? 10. In Box City, an influenza vaccine was tested on 1,000 people, 400 males and 600 females. Of the males, 50% contracted influenza after vaccination versus 30% of the females. Calculate and interpret the risk ratio of females compared to males of contracting influenza. 11.
An advertising agency collected a random sample of 300 businesses targeted with an advertising campaign for a large commercial bank. The sample was used to investigate the efficacy of the advertising campaign. One of the variables measured was whether the business was considering becoming a client of the bank. Of the businesses sampled, 50 of the 300 businesses reported that they were considering becoming a client of the bank. A hypothesis test was conducted to determine if this provides evidence that less than 20% of all businesses were considering becoming a client of the bank. Calculate the test statistic to two decimal places (2dp). Test statistic =
A researcher took a random sample of 200 new mothers in the United States (Group 1) and found that 16% of them experienced some form of postpartum depression. Another random sample of 200 new mothers in France (Group 2), where mothers receive 16 weeks of paid maternity leave, found that 11% experienced some form of postpartum depression. Can it be concluded that the percent of women in the United States experience more postpartum depression than the percent of women in France? Use α=0.05. Select the correct alternative hypothesis and decision
A basketball coach is interested in determining if shooting free throws underhand is better than shooting them using the overhead method. He has four high school teams (two boys' teams and two girls' teams, with 13 players on each team) available to take part in an experiment. He believes that the difference in shooting percentages will vary more for boys than for girls. He randomly chooses and instructs half of the boys to continue shooting free throws overhead and the rest of the boys to shoot underhand. He does the same for the girls. At the end of a six-game summer league, he compares the shooting percentages for the overhead shooting boys to the underhand shooting boys and the overhead shooting girls to the underhand shooting girls. (a) What is the advantage of using a block design for this study? O Blocking by gender will reduce the variation in the response variable by creating homogeneous groups and determining the effect of the new shooting style on the response (percentage of…
A study was conducted to compare oral and intravenous antibiotics in patients with lower respiratory tract infection. Patients were rated in terms of their final outcome after their assigned treatment (delivery route of antibiotic). The outcomes were classified as: cure (1), partial cure (2), antibiotic extended (3), antibiotic changed (4), death (5). Note that this variable is categorical and ordinal. For the oral delivery group, the numbers of patients falling into the five outcome levels were: 74, 68, 16, 14, and 9, respectively. The following are some graphical summaries. FREQUENCY FREQUENCY of OUTCOME 80 70 60 50 40 30 20 10 0 1 2 3 4 5 OUTCOME 28 68 1 74 16 HA 14 9 What are the names of the two types of graphics and what data is each of them displaying to us?
The management of Choices Inc. can pay bonuses for customer service staff based on feedback scores or based on reversed cancellations. Good feedback and reversed cancellations both generate $12,000 in additional profit for the company. A hard-working employee has a 75% chance of getting a positive score, but only a 50% chance of reversing a cancellation, If the employee fails to put in full effort, then the likelihood of a positive score or a reversed cancellation is, in both cases, 25%. Assume an employee's utility function for income w is u(w) = sart(w), and the effort cost from working hard (in utility units) is 10. With a base wage of 10,000, how much more profitable is Choices Inc. with bonuses based on feedback, instead of reversed cancellations? (1.e. what is the difference in profit if the manager always offers the smallest bonus that will induce the employee to work hard?) O $3,000 O $4,500 O $9,000 $12,000
Determine whether the results appear to have statistical significance, and also determine whether the results appear to have practical significance. In a study of a birth sex selection method used to increase the likelihood of a baby being born female, 1942 users of the method gave birth to 948 males and 994 females. There is about a 15% chance of getting that many babies born female if the method had no effect. Because there is a 15% chance of getting that many babies born female if the method had no effect, the method does not have statistical significance. Not many couples would likely use a procedure that raises the likelihood of a baby born female from the approximately 50% rate expected by chance to the 51.2 % produced by this method. (Round to the nearest integer as needed.) So, this method does not have practical significance.
USE THE 8-STEP HYPOTHESIS TESTING Refer to the study by Carter et al. [A-9], who investigated the effect of age at onset of bipolar disorder on the course of the illness. One of the variables studied was subjects' family history. Table 3.4.1 shows the frequency of a family history of mood disorders in the two groups of interest: early age at onset (18 years or younger) and later age at onset (later than 18 years). Family History of Mood Disorders Early ≤ 18(E) 28 19 41 53 Later > 18 (L) 35 38 44 60 141 Total 63 57 85 113 Negative (A) Bipolar disorder (B) Unipolar (C) Unipolar and bipolar (D) Total 177 318 Source: Tasha D. Carter, Emanuela Mundo, Sagar V. Parkh, and James L. Kennedy, "Early Age at Onset as a Risk Factor for Poor Outcome of Bipolar Disorder," Journal of Psychiatric Research, 37 (2003), 297-303. Can we conclude on the basis of these data that subjects 18 or younger differ from subjects older than 18 with respect to family histories of mood disorders? Let a = .05.

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