In a random sample of 80 components of a certain type, 28 are found to be defective. (a) Give a point estimate of the proportion of all such components that are not defective. (b) A system is to be constructed by randomly selecting two of these components and connecting them in series, as shown here. The series connection implies that the system will function if and only if neither component is defective (i.e., both components work properly). Estimate the proportion of all such systems that work properly. [Hint: If p denotes the probability that a component works properly, how can P(system works) be expressed in terms of p?] (Enter your answer to four decimal places.)

In a random sample of 80 components of a certain type, 28 are found to be defective. (a) Give a point estimate of the proportion of all such components that are not defective. (b) A system is to be constructed by randomly selecting two of these components and connecting them in series, as shown here. The series connection implies that the system will function if and only if neither component is defective (i.e., both components work properly). Estimate the proportion of all such systems that work properly. [Hint: If p denotes the probability that a component works properly, how can P(system works) be expressed in terms of p?] (Enter your answer to four decimal places.)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.5: Systems Of Linear Equations In More Than Two Variables

Problem 27E

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A medical researcher claims that the proportion of patients receiving 200 mg of a newly-developed influenza vaccine who go on to contract influenza strain X is less than the proportion of patients receiving 200 mg of last year's influenza vaccine who contract influenza strain X. Of 320 patients who are given last year's vaccine, 114 contract influenza strain X. Of 350 patients who are given the new vaccine, 112 of them contract influenza strain X. Let PN be the proportion of patients receiving the newly-developed vaccine and pL be the proportion of patients receiving last year's vaccine. State the null and alternative hypotheses and the value of the test statistic. Ho: PN =PL versus HA: PN > PL; Test statistic: Z = 0.99 Ho: PN=PL versus HA: PN > PL; Test statistic: Z = 1.55 Ho: PN-PL versus HA: PN PL; Test statistic: Z= 1.55 Ho: PN-PL versus HA: PN PL; Test statistic: Z= 0.99

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