Currently it is estimated that 2 out of every 1000 Californians are infected withcoronavirus. The so-called rapid "antigen" test for coronavirus has a very low falsepositive rate of just 0.02, but has a high false negative rate of 0.27. The so-calledPCR test is more reliable: it has an even lower false positive rate than the antigentest, namely only 0.001, but even more importantly its false negative rate is muchlower at 0.01.What is the probability that you have a coronavirus infection conditional on yourPCR test has coming back positive?

Answered: Image /qna-images/answer/c41f1117-37e7-4f4d-8d4f-548c379eccda.jpg

Answered: Currently it is estimated that 2 out of…

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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Historically, the proportion of people who trade in their old car to a car dealer when purchasing a new car is 48%. Over the previous six months, in a sample of 115 new car buyers, 46 have traded in their old car. To determine (at the 10% level of significance) whether the proportion of new car buyers that trade in their old car has this is statistically significantly decreased, what can you conclude concerning the null hypothesis? A) reject the null hypothesis Or B) fail to reject the null hypothesis
It is easier to reject the null hypothesis if the researcher uses a smaller alpha (α) level. choose True or False?
An alpha level of 0.05 means that 99% of the means are likely to reflect the null hypothesis. True False
Researchers at the University of Boston's Children's Hospital and Harvard Medical School analyzed records of breast cancer screening and diagnostic evaluations.† Discussing the downsides of the screening process, the article states that the rate of false-positives is higher than previously thought, and that false-positives lead to unnecessary medical follow-up that can be costly. Suppose that screening is used to decide between a null hypothesis of H0: no cancer is present and an alternative hypothesis of Ha: cancer is present. (Although these are not hypotheses about a population characteristic, this exercise illustrates the definitions of Type I and Type II errors.) Would a false-positive (thinking that cancer is present when in fact it is not) be a Type I error or a Type II error? a. Type I error b. Type II error b. Describe a Type I error in the context of this problem, and discuss the possible consequences of making a Type I error. a. Coming to the…
A researcher wants to compare the effectiveness of two treatments on a sample of 25 patients. What is the null hypothesis for the Wilcoxon Signed-Ranks Test?
there is 0.01 and 0.05 alpha level, what is the critical cutoff z scores for both? which one is easier to reject the null hypothesis and why?
The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.8 auto accidents per day with a variance of 0.0016. The actuaries of the company claim that the variance of the number of accidents per day is no longer equal to 0.0016. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test. Ho:____ H1:____
A major credit card company is interested in the proportion of individuals who use a competitor’s credit card. Their null hypothesis is H0: p=0.65H0: p=0.65, and based on a sample they find a sample proportion of 0.70 and a pp-value of 0.053. Is there convincing statistical evidence at the 0.05 level of significance that the true proportion of individuals who use the competitor’s card is actually greater than 0.65 ?
Recently, a large academic medical center determined that 7 of 15 employees in a particular position were male,whereas 56% of the employees for this position in the general workforce were male. At the 0.01 level of significance, is there evidence that the proportion of males in this position at this medical center is different from what would be expected in the general workforce? What are the correct hypotheses to test to determine if the proportion is different? A. H0:π≥0.56; H1:π<0.56 B. H0:π=0.56; H1:π≠0.56 C.H0:π≤0.56; H1:π>0.56 D.H0:π≠0.56; H1:π=0.56 Part 2 Calculate the test statistic. ZSTAT=enter your response here (Type an integer or a decimal. Round to two decimal places as needed.) Part 3 What is the p-value? The p-value is..... (Type an integer or a decimal. Round to three decimal places as needed.) State conclusion of test Reject/Do not reject the null hypothesis. There is sufficient/insufficient evidence to…
It is known that for right-handed people, the dominant (right) hand tends to be stronger. For left-handed people who live in a world designed for right-handed people, the same may not be true. To test this, muscle strength was measured on the right and left hands of a random sample of 15 left-handed men and the difference (left - right) was found. The alternative hypothesis is one-sided (left hand stronger). The resulting t-statistic was 1.80. Assuming the conditions are met, based on the t-statistic of 1.80 the appropriate conclusion for this test using α = .05 is
A survey of 90 recently delivered women on the rolls of a county welfare department revealed that 27 had a history of intrapartum or postpartum infection. Can we conclude that the population proportion with a history of intrapartum or postpartum infection is significantly less than or equal to 0.25? Let alpha = 0.05.
We tested to see if people who consumed caffeine had a lower average reaction time than those who didn’t consume caffeine at the alpha = 0.08 level. Assume we found a p-value of 0.5437. Which below would be an appropriate conclusion and interpretation? With an alpha of 0.08, and a p-value of 0.5437, we fail to reject the null and state we have insufficient evidence to support that the true average reaction time of caffeine consumers was less than that of non-caffeine consumers. With an alpha of 0.08, and a p-value of 0.5437, we reject the null and state we have sufficient evidence to support that the true average reaction time of caffeine consumers was less than that of non-caffeine consumers. With an alpha of 0.08, and a p-value of 0.5437, we fail to reject the null and state we have sufficient evidence to support that the true average reaction time of caffeine consumers was less than that of non-caffeine consumers. With an alpha of 0.08, and a p-value of 0.5437, we…

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