1 Two groups of patients, suffering from the same medical condition, took part in a clinicaltrial of a new drug. One of the groups was given the drug whilst the other group was givena placebo, a drug that has no physical effect on their medical condition.The table shows the number of patients in each group and whether or not their conditionimproved.Condition improvedCondition did not improvePlacebo2055Drug4629Conduct a x² test, at the 5% level of significance, to determine whether the condition of thepatients at the conclusion of the trial is associated with the treatment that they were given.

Given data: Placebo Drug Condition improved 20 46 Condition did not improve 55 29

Answered: 1 Two groups of patients, suffering…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 2EQ: 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed...

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Explain the differences between Gaussian elimination and Gauss-Jordan elimination.
2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1
MSA Computer Corporation manufactures two models of smartphones, the Alpha 4 and the Beta 5. The firm employs five technicians, working 160 hours each per month, on its assembly line. Management insists that full employment (i.e., all 160 hours of time) be maintained for each worker during next month’s operations. It requires 20 labor hours to assemble each Alpha 4 computer and 25 labor hours to assemble each Beta 5 model. MSA wants to see at least 10 Alpha 4s and at least 15 Beta 5s produced during the production period. Alpha 4s generate $1,200 profit per unit, and Beta 5s yield $1,800 each. Determine the most profitable number of each model of smartphone to produce during the coming month. Formulate as an LP problem. Solve using an LP software program or spreadsheet.
Suppose a birth defect has a recessive form of inheritance.In a study population, the recessive gene (a) initially has aprevalence of 25%. A subject has the birth defect if bothmaternal and paternal genes are of type a. A further study finds that after 10 generations (≈200 years)a lot of inbreeding has taken place in the population. Twosubpopulations (populations A and B), consisting of 30%and 70% of the general population, respectively, haveformed. Within population A, prevalence of the recessivegene is 40%, whereas in population B it is 10%. Suppose that a baby is born with a birth defect,but the baby’s ancestry is unknown. What is the posteriorprobability that the baby will have both parents from population A, both parents from population B, or mixed ancestry,respectively? (Hint: Use Bayes’ rule.)
2. A new chemotherapy drug is released to treat leukemia and researchers suspect that the drug may have fewer side effects than the most commonly used drug to treat leukemia. The two drugs have equivalent efficacy. In order to determine if a larger study should be conducted to look into the prevalence of side effects for the two drugs, set up a Mann-Whitney U test at the alpha equals .05 level and interpret its results.Number of Reported Side-EffectsOld Drug 0 1 3 3 5New Drug 0 0 1 2 4 A) We fail to reject H0, which states the two populations are equal at the alpha equals .05 level because the calculated U value of 16.5 is greater than the critical U value of 2.B) We fail to reject H0, which states the two populations are equal at the alpha equals .05 level because the calculated U value of 8.5 is greater than the critical U value of 2.C) We reject H0 in favor of H1, which states the two populations are not equal at the alpha equals .05 level because the calculated U value of 16.5 is…
The viruses causing problems in strawberry plants are mainly spread by one insect, the strawberry aphid. Carly believes that as aphids feed on leaves, they transmit viruses that can cause a rapid decrease in plant growth. She decides to verify whether or not the number of strawberry aphids found on a plant could be linked to its growth. She therefore randomly chooses 5 strawberry plants at the same stage of development in a virus-infested garden. For each individual plant, she first collects all the aphids present on the plant and weighs them, and then weighs the entire plant to have a measure of plant growth. She obtains the following data. (Attach on side) Is Carly correct in thinking that when the number of aphids on a plant is larger, the growth of the plant is affected (i.e., its weight is smaller)? Apply the appropriate statistical method with a test of significance at α = 0.05.
3.Luijckx et al (2012) discovered that resistance to the bacterial parasite Pasteuria ramose is genetically variable in the common freshwater crustacean, Daphnia magna. To investigate the genetic basis of this variation, they crossed a completely resistant lineage to a completely susceptible lineage. All the F1 offspring were resistant. These offspring, when mature, were then crossed to each other to produce an F2 generation. If resistance is the result of only a single gene with two forms (alleles) then resistant and susceptible F offspring should occur in a 3:1 ratio. Of 71 F2’s tested, 57 were resistant and 14 were susceptible. a.With these data, calculate the range of most plausible-values for the proportion of resistant offspring. Does the plausible range include the proportion predicted if resistance is determined by a single gene? b.Give two other values for proportion that are also consistent with the data. c.Test the genetic hypothesis. Are the results compatible with the…
A certain company produces fidget spinners with ball bearings made of either plastic or metal. Under standard testing conditions, fidget spinners from this company with plastic bearings spin for an average of 2.7 minutes, while those from this company with metal bearings spin for an average of 4.2 minutes. A random sample of three fidget spinners with plastic bearings is selected from company stock, and each is spun one time under the same standard conditions; let x¯1x¯1 represent the average spinning time for these three spinners. A random sample of seven fidget spinners with metal bearings is selected from company stock, and each is likewise spun one time under standard conditions; let x¯2x¯2 represent the average spinning time for these seven spinners. What is the mean μ(x¯1−x¯2)μ(x¯1−x¯2) of the sampling distribution of the difference in sample means x¯1−x¯2x¯1−x¯2 ? 3(2.7)−7(4.2)=−21.33(2.7)−7(4.2)=−21.3 A 3−7=−43−7=−4 B 2.7−4.2=−1.52.7−4.2=−1.5 C…
MSA Computer Corporation manufactures two models of minicomputers, the Alpha 4 and the Beta 5. The firm employs five technicians, working 160 hours each per month, on its assembly line. Management insists that full employment (i.e., all 160 hours of time) be maintained for each worker during next month’s operations. It requires 20 labor hours to assemble each Alpha 4 computer and 25 labor hours to assemble each Beta 5 model. MSA wants to see at least 10 Alpha 4s and at least 15 Beta 5s produced during the production period. Alpha 4s generate $1,200 profit per unit, and Beta 5s yield $1,800 each. Determine the most profitable number of each model of minicomputer to produce during the coming month.
22. Is there multicollinearity in the model? Yes, No or Cannot be determined?
A random sample of 1000 people with known allergies to poison ivy participated in a recent study. Oil from the poison ivy plant was rubbed on a patch of skin. For 500 of the subjects, the oil it was washed off within 5 minutes. For the other 500 subjects, the oil was washed off after 5 minutes. Observed reactions were recorded as "none," "mild," or "strong." The results are summarized in the following table. Reaction Within 5 Minutes After 5 Minutes Row Total NoneMildStrong 4056530 48326126 453391156 Column Total 500 500 1000 Suppose a person selected at random from this sample of 1000 subjects. What is the probability that a strong reaction was observed, given that the oil was washed off within 5 minutes?
A school Psychologist is interested in the effect of violent television programs on a child's agression depending on if the show is a cartoon or not. Eighty children were recruited and were divided into equal groups. Half of the children watched a violent television program while the other half watched a non- violent program. Half of the children watched a cartoon while the other half watched a show that was not a cartoon. The children were then placed in a small group and the researcher measured the level of agressiveness of each child. A) z- test B) t - test C) test independent samples D) T - TEST RELATED SAMPLES E) ANOVA F) FACTORIAL ANOVA G) repeated measures ANOVA H) pearson correlation i) chi square

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