A grocery supplier has two potato fields, A and B, growing the same kind ofpotato. However the field A produces potato with proportion of 0=3% ofpotatoes that are rotten inside, while field B produces 0=6% of rotten potatoes.The grocery manager asked the supplier to deliver potato from field A. Thedelivery arrived. The manager is bayesian and based on her prior experiencewith the supplier, she believes that the probability of the delivery being fromfield A (i.e. that the supplier is honest) is 40%. While the supplier hasn't left yet,the manager quickly checks 18 potatoes and discovers x = 2 of them to berotten.Find the posterior probability P(0 = 0.03 | x = 2) that the potato comesfrom the field A, after finding 2 rotten potatoes in the sample.0.0650.1130.640.2510.216

we need to apply Bayes' theorem to find the posterior probability that the potatoes come from field…

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.
Dr. Mackintosh believes a new olfactory therapy would be more successful in promoting weight loss among obese patients. His patients are first weighed and then randomly assigned to olfactory therapy, dance therapy, or a control condition. At the end of the three weeks, the amount of weight lost is recorded. The results indicate no significant difference in the amount of weight lost between the three conditions. If true differences existed between the conditions, but they were not detected, what kind of error occurred?
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 =
Lucy recently asked the servers at her restaurant to only give straws to customers who request them. She thinks that about half of the customers will ask for straws but hopes that the rate will be less than half. She randomly selects 100 customers and finds that 43 of them ask for a straw. To determine if these data provide convincing evidence that the proportion of customers who will ask for a straw is less than 50%, 150 trials of a simulation are conducted. Lucy is testing the hypotheses: H0: p = 50% and Ha: p < 50%, where p = the true proportion of customers who will ask for a straw. Based on the results of the simulation, what is the estimate of the P-value of the test? A) 0.0333 B) 0.05 C) 0.0733 D) 0.11
I need help with #3 please.
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 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?
2. A researcher had rats engage in a lever-press task for either a small, medium, or larger reward. The number of lever presses was the dependent variable. The data were as follows: Reward Size Small Medium Large 1 4 6 4 3 5 1 4 4 2 5 T = 13 SS = 2.75 T= 6 T= 20 SS = 9 SS = 2 EX2 = 165 a. Do the data indicate that reward size had a significant impact on lever-pressing? Use the hypothesis testing steps & p = .05. Compute any necessary post-hoc tests. b. Compute eta-squared to measure the effect size.
The National Institute of Mental Health published an article stating that in any one-year period, approximately 8.8% of American adults suffer from depression or a depressive illness. Suppose that in a survey of 2000 people in a certain city, 11.3% of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that city suffering from depression or a depressive illness is more than the 8.8% in the general adult American population. Test the relevant hypotheses using a 5% level of significance. Give answer to at least 4 decimal places. a. What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.) H0: H1: b. Based on the hypotheses, find the following: c. Test Statistic = d. p-value = e. Based on the above we choose to:_____________ f. The correct summary would be: ____________ that the true proportion of people in that city suffering from depression or a…
▾ Part 1 of 4 A pharmaceutical company claims their new diabetes medication results in less variance in a patient's glucose level than if the patient were on no medication at all. An endocrinologist wishes to test this claim. She divides participants randomly into two groups. Group A consists of 20 diabetics who received the medication; group B consists of 26 diabetics who received a placebo. After two weeks, the blood sugar level of each patient in each group was measured with the following results (in mg/dL): Group A: 77.8, 229.4, 199.9, 110.1, 180.2, 116.1, 139.7, 171.1, 37.4, 158.1, 88.4, 195.5, 246.1, 142.4, 178.1, 105.5, 179.6, 146.1, 78.8, 123.7 Group B: 124.5, 130.1, 136, 162.8, 113.4, 72.8, 142.6, 50.3, 179.8, 197, 230, 194.3, 171, 109.3, 114.4, 107.5, 114.7, 195.3, 127.7, 126.4, 85.6, 166.7, 182.3, 113.5, 216.7, 162.8 Perform a hypothesis test using a 6% level of significance to test the pharmaceutical company's claim. Step 1: State the null and alternative hypotheses. Ho:…

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