Bonus Problem (+1pt) Bayes' Theorem became extremely "popular" during the CoViD-19 pandemic. Astudy published in late 2021 calculated the probability of a false negative RT-PCR test during the earlystages of the disease to be approximately 58%. It has however a very high specificity of approximately95%, meaning that the percentage of false positives is at 5%. Assuming that the positivity rate is anaccurate measure of the true infected population, calculate the probability that a person selected atrandom has not contracted SARS-CoV-2, when their PCR test is negative, and the positivity rate is(a) 4%(b) 12%

Let the events "a" and "p" represent the actual negative and actual positive respectively. Also, let…

Answered: Bonus Problem (+1pt) Bayes' Theorem…

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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When the Titanic sank, passenger survival rates were recorded along with additional information like their name, what class ticket they had, their age, and whether or not they had children. Some of these factors may predict whether or not a passenger was likely to survive the accident. The data set "Titanic survival.jasp" contains actual recorded data from the event. Using the variables "Class" and "Survived", conduct a Chi-Square Test for Independence, at alpha = 0.05, to see if a passengers ticket class (first, second, or third class) is significantly associated with their survival rates. Identify the correct value for df. A. 2 B. 1309 C. 4 D. 127
The standard error of most sample estimators approaches zero as the sample size increases, so almost any difference between the sample statistic and the hypothesized parameter value, no matter how tiny, will be significant if the sample size is large enough. Researchers who deal with large samples must expect “significant” effects, even when an effect is too slight to have any practical importance. Is an improvement of 0.2 mpg in fuel economy important to Toyota buyers? Is a 0.5 percent loss of market share important to Hertz? Is a laptop battery life increase of 15 minutes important to Dell customers? Such questions depend not so much on statistics as on a cost/benefit calculation. Since resources are always scarce, a dollar spent on a quality improvement always has an opportunity cost (the foregone alternative). If we spend money to make a certain product improvement, then some other project may have to be shelved. Since we can’t do everything, we must ask whether a proposed product…
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A random sample of size n = 178 is taken from a population of size N = 3,718 with mean μ = −80 and variance σ2 = 190. [You may find it useful to reference the z table.] a-1. Is it necessary to apply the finite population correction factor? Yes No a-2. Calculate the expected value and the standard error of the sample mean. (Negative values should be indicated by a minus sign. Round "standard error" to 2 decimal places.) b. What is the probability that the sample mean is between −82 and −78? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.) c. What is the probability that the sample mean is greater than −79? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)
Only 15% of registered voters voted in the last election. Will voter participation increase for the upcoming election? Of the 363 randomly selected registered voters surveyed, 58 of them will vote in the upcoming election. What can be concluded at the αα = 0.01 level of significance? For this study, we should use Select an answer t-test for a population mean z-test for a population proportion The null and alternative hypotheses would be: H0:H0: ? μ p Select an answer > < ≠ = (please enter a decimal) H1:H1: ? μ p Select an answer = < ≠ > (Please enter a decimal) The test statistic ? t z = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is ? > ≤ αα Based on this, we should Select an answer accept reject fail to reject the null hypothesis. Thus, the final conclusion is that ... The data suggest the population proportion is not significantly higher than 15% at αα = 0.01, so there…
Question 39 1 In a one-way ANOVA, if the computed F value exceeds the critical F value, what decision is made regarding the null hypothesis? O Reject Ho since there is evidence of a treatment effect. O Do not reject Ho since there is no evidence of a difference. O Do not reject Ho because a mistake has been made. O Reject Ho since there is evidence that all means differ.
We want to use a z-test to determine if the sample mean is greater than 20 at the alpha = 0.05. What is the critical value(s)?
A test for SARS-Cov-2 has sensitivity of 0.8 and specificity of 0.7. a. A person tested positive in the test, what is the probability that they have the virus?
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