A disease strikes 1 in 25 students. A new test correctly diagnoses if one has it...

A disease strikes 1 in 25 students. A new test correctly diagnoses if one has it 95% of the time and correctly confirms that one does not have it 97% of the time. If you tested positively for the it, what is the probability that you actually have it?

Solutions

Expert Solution

P(have the disease) = 1/25 = 0.04

P(test positive) = P(test positive | have the disease) * P(have the disease) + P(test positive | does not have the disease) * P(does not have the disease)

= 0.95 * 0.04 + 0.97 * (1 - 0.04)

= 0.9692

P(have the disease | test positive) = P(test positive | have the disease) * P(have the disease)/P(test positive)

= (0.95 * 0.04)/0.9692

= 0.0392

orchestra answered 1 year ago

Next > < Previous

Related Solutions

A new diagnostics test is proposed for COVID19. this test correctly identifies infected people 99% of...

A new diagnostics test is proposed for COVID19. this test correctly identifies infected people 99% of the times and identifies uninfected people 80% of the times. Then, Type I error and Type I error for this test is ____ and ____ respectively.

Write two nursing diagnoses for the client who has Crohn’s disease and gastritis, looking for similarities...

Write two nursing diagnoses for the client who has Crohn’s disease and gastritis, looking for similarities and differences between the treatment and nursing interventions. Include one for discharge planning.

1. The mean age of College students is 25. A certain class of 33 students has...

1. The mean age of College students is 25. A certain class of 33 students has a mean age of 22.64 years. Assuming a population standard deviation of 2.87 years, at the 5% significance level, do the data provide sufficient evidence to conclude that the mean age of students in this class is less than the College mean? a. Set up the hypotheses for the one-mean ?-test. ?0: ??: b. Compute the test statistic. Round to two decimal places. c....

Assume there is a medical test to diagnose a disease. If a person has the disease,...

Assume there is a medical test to diagnose a disease. If a person has the disease, the probability of having positive test result is 98 percent. If a person does not have the disease, the probability of having negative test results is 99.6 percent. The probability that a person has a disease is 1 percent in the population. Answer the following questions: a) If a person has a positive test result, what is the probability that he/she has the disease?...

A new medical test has been designed to detect the presence of the mysterious Brainlesserian disease....

A new medical test has been designed to detect the presence of the mysterious Brainlesserian disease. Among those who have the disease, the probability that the disease will be detected by the new test is 0.78. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.02. It is estimated that 19 % of the population who take this test have the disease. If the test administered...

The prevalence of a disease D in the population is 10%. A new test is introduced...

The prevalence of a disease D in the population is 10%. A new test is introduced by a laboratory with the following characteristics. The laboratory notes that if someone has the disease, his or her test will be positive 90% of the time (P(pos|D) = 0.90). However, a completely healthy individual will test positive with probability 0.06 (P (pos|Dc) = .06). (a) If we randomly select 5 people from this population, what is the probability that all of them...

1. You have sampled 25 randomly selected students to find the mean test score. A 95%...

1. You have sampled 25 randomly selected students to find the mean test score. A 95% confidence interval for the mean came out to be between 85 and 92. Which of the following statements gives a valid interpretation of this interval? 1)If this procedure were to be repeated many times, 95% of the confidence intervals found would contain the true mean score. 2)If 100 samples were taken and a 95% confidence interval were found, 95 of them would be between...

A multiple choice test has four possible responses. To test whether this question was answered correctly...

A multiple choice test has four possible responses. To test whether this question was answered correctly by more people than would be expected due to chance, a hypothesis test of 400 student answers is conducted. What is the null and alternative hypothesis (in words and symbols). If 218 of the 400 students got the correct response, what is the p-value? Explain your method and TI commands. What decision is made if a significance level of 0.01 is used? Based on...

1. For 25 randomly selected students, ( a) how many ways do all the 25 students...

1. For 25 randomly selected students, ( a) how many ways do all the 25 students have different birthday? b) find the probability that at least two students have the same birthday. c) find the probability that only two share the same birthday. d) for probability computed above identify the sample space, the experiment and outcomes. e) can a random variable be used for the case above? If yes list the possible values for the variable. I figured out a...

Dartnose College has 4000 students. 30% are first-year students, 25% are sophomores, 25% are juniors, and...

Dartnose College has 4000 students. 30% are first-year students, 25% are sophomores, 25% are juniors, and 20% are seniors. 40% of the first-year students are women, 60% of the sophomores are women, 40% of the jumiors are women, and 60% of the seniors are women. Every student is in one and only one of these classes. 1. What is the probability that a randomly selected student will NOT be a junior? 2. What is the probability that a randomly selected...

Subjects