math 410 lab 7

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Drexel University *

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410

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Statistics

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Jan 9, 2024

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Uploaded by madnan12678

Exercise 2.1 pnorm( 𝑥 , 𝜇 , 𝜎 ) pnorm(2,3.25,.75) 0.04779035 By hand: z = (x-μ)/σ z=(2-3.25)/.75 z=-1.6667 Probability table=.0485 Exercise 2.2 pnorm( 𝑥 , 𝜇 , 𝜎 ) pnorm(45,36,3.5) 0.994936 1-pnorm(45,36,3.5) 0.005063995 By hand: z = (x-μ)/σ z=(45-36)/3.5 z=2.57 Probability table=.9949 1-.9949 = .0051 Exercise 2.3 pnorm( 𝑥 , 𝜇 , 𝜎 )-pnorm( 𝑥 , 𝜇 , 𝜎 ) pnorm(79,72,3)-pnorm(77,72,3) 0.03797502 By hand: z = (x-μ)/σ z=(77-72)/3 z=1.6667 Probability table=.9515

By hand: z = (x-μ)/σ z=(79-72)/3 z=2.333 Probability table=.9901 .9901-.9515= .0386 Exercise 2.4 score=c(90:100) pnorm(score,84,5) [1] 0.8849303 0.9192433 0.9452007 0.9640697 0.9772499 0.9860966 0.9918025 [8] 0.9953388 0.9974449 0.9986501 0.9993129 The minimum score to get is 91% z = (x-μ)/σ z=(90-84)/5 z=1.2 Probability table=.8849 Repeat for numbers 90-100 91: 1.4 and the probability is 0.9192 92: 1.6 and the probability is 0.9452 93: 1.8 and the probability is 0.9641 94: 2.0 and the probability is 0.9772 95: 2.2 and the probability is 0.9861 96: 2.4 and the probability is 0.9918 97: 2.6 and the probability is 0.9953 98: 2.8 and the probability is 0.9974 99: 3.0 and the probability is 0.9987 100: 3.2 and the probability is 0.9993

Exercise 2.5 pnorm(0,72,3) pnorm(-1,72,3) 4.351951e-131 This is not a problem for other data because the z-scores are not as small as they were for this problem. This is due to the fact that the raw score and the mean are very different in size which causes the z score to be very small thus not being able to use the distribution table. Exercise 3.1 R1=c(6,1) R2=c(1,6) data=matrix(c(R1,R2),nrow=2,byrow=T) fisher.test(data,alternative="greater") data: data p-value = 0.01457 alternative hypothesis: true odds ratio is greater than 1 95 percent confidence interval: 1.721066 Inf sample estimates: odds ratio 23.4961 The R answer is similar to the final answer that is from the book.

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