Allergic reactions to poison ivy can be miserable. Plant oils cause the reaction. Researchers at Allergy Institute did a study to determine the effects of washing the oil off within 5 minutes of exposure. A random sample of 1000 people with known allergies topoison ivy participated in the study. Oil from the poison ivy plant was rubbed on a patch of skin. For 500 of the subjects, it was washed off within 5 minutes. For the other 500 subjects, the oil was washed off after 5 minutes. The results are summarized in thefollowing table.Within 5 Minutes4205525500Let's use the following notation for the various events: W = washing oil off within 5 minutes, A = washing oil off after 5 minutes, N = no reaction, M = mild reaction, S = strong reaction. Find the following probabilities for a person selected at random from thissample of 1000 subjects. (Use 3 decimal places.)(a) P(N)P(M)P(S)ReactionNoneMildStrongColumn Total(b) P(N | W)P(S | W)(c) P(NA)P(S | A)(d) P(Na W)P(M and W)After 5 Minutes40348112500(e) P(N or M).Row Total4604031371000Are the events N = no reaction and M = mild reaction mutually exclusive? Explain.O No. P(N and M) = 0.O Yes. P(N or M) = 0.O No. P(N or M) * 0.O Yes. P(N and M) = 0.(f) Are the events N = no reaction and W = washing oil off within 5 minutes independent? Explain.O No. P(N and W) = P(N) P(W).O Yes. P(N and W) P(N) P(W).O Yes. P(N and W) = P(N) P(W).O No. P(N and W) P(N) P(W).

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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 recent study investigated whether cell phone users experience separation anxiety when they cannot access their phones. Because blood pressure increases with anxiety, the researchers used systolic blood pressure as an operational measure of anxiety. The experiment involved a random sample of cell phone users that were divided into two groups at random. One group of participants completed a survey while their phones were locked in a cabinet in a separate room and the other group of participants completed the same survey while their phones were nearby. (The survey questions were unrelated to cell phone use.) At the end of the survey, theresearchers measured each participant's systolic blood pressure. The same experiment was conducted in Montreal, Toronto, Vancouver, and St. Zotique. The blood pressure data needed is below. Use these data to answer the following question: compute r2 for the data collected in st. zotique. Please answer to 5 decimal places. Cell Phone (CP) No Cell Phone…
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Phosphorous is a chemical that is found in many household cleaning products. Unfortunately, phosphorous also finds its way into surface water, where it can harm fish, plants, and other wildlife. Two methods of phosphorous reduction are being studied. At a random sample of 7 locations, both methods were used and the total phosphorous reduction (mg/L) was recorded. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer. Things that are labelled i underneath a b c, etc are all part of that part.
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A recent study investigated whether cell phone users experience separation anxiety when they cannot access their phones. Because blood pressure increases with anxiety, the researchers used systolic blood pressure as an operational measure of anxiety. The experiment involved a random sample of cell phone users that were divided into two groups at random. One group of participants completed a survey while their phones were locked in a cabinet in a separate room and the other group of participants completed the same survey while their phones were nearby. (The survey questions were unrelated to cell phone use.) At the end of the survey, theresearchers measured each participant's systolic blood pressure. The same experiment was conducted in Montreal, Toronto, Vancouver, and St. Zotique. The blood pressure data for all participants needed are below. Use these data to answer the following question: comoute the estimated standard error of d for the data collected in toronto. Please answer to 5…
Phosphorous is a chemical that is found in many household cleaning products. Unfortunately, phosphorous also finds its way into surface water, where it can harm fish, plants, and other wildlife. Two methods of phosphorous reduction are being studied. At a random sample of 7 locations, both methods were used and the total phosphorous reduction (mg/L) was recorded. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer. Site 1 2 3 4 5 6 7 Method I: 0.013 0.020 0.015 0.055 0.007 0.002 0.010 Method II: 0.014 0.045 0.017 0.039 0.017 0.001 0.013 Do these data indicate a difference (either way) in the average reduction of phosphorous between the two methods? Use α = 0.05. (Let d = Method I − Method II.) (i) What is the level of significance? What is the value of the sample test statistic? (Round…

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