Let p be the probability that your printer operates successfully for a job, and suppose that the operation is independent across jobs. You have printed 20 jobs in a day, and all are successful. a. You want to find out how reliable your printer is. The point estimate for the reliability p is just 1, and the standard error is 0. We know a printer cannot always work, so this approach clearly fails. Instead, test the hypothesis Ho :p = Po HA :p > Po VS = 0.92. First write down the formula for calculating at the 0.05 significance level, where po the p-value. Then use pbinom to find the p-value for this problem. b. Create a confidence interval for the success probability p by inverting the hypothesis test (namely, the confidence interval contains all po so that you do not reject Ho; for code implementation, discretize the candidate po E [0, 1]). This interval estimate is a more reasonable assessment of the reliablity than the point estimate. c. Use binom.test to verify your result in the last part.
Let p be the probability that your printer operates successfully for a job, and suppose that the operation is independent across jobs. You have printed 20 jobs in a day, and all are successful. a. You want to find out how reliable your printer is. The point estimate for the reliability p is just 1, and the standard error is 0. We know a printer cannot always work, so this approach clearly fails. Instead, test the hypothesis Ho :p = Po HA :p > Po VS = 0.92. First write down the formula for calculating at the 0.05 significance level, where po the p-value. Then use pbinom to find the p-value for this problem. b. Create a confidence interval for the success probability p by inverting the hypothesis test (namely, the confidence interval contains all po so that you do not reject Ho; for code implementation, discretize the candidate po E [0, 1]). This interval estimate is a more reasonable assessment of the reliablity than the point estimate. c. Use binom.test to verify your result in the last part.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 39E: Assume that the probability that an airplane engine will fail during a torture test is 12and that...
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![Let p be the probability that your printer operates successfully for a job, and suppose that the
operation is independent across jobs. You have printed 20 jobs in a day, and all are successful.
a. You want to find out how reliable your printer is. The point estimate for the reliability p is just
1, and the standard error is 0. We know a printer cannot always work, so this approach
clearly fails. Instead, test the hypothesis
Họ :p = Po
HA :p > Po
VS
0.92. First write down the formula for calculating
at the 0.05 significance level, where po
the p-value. Then use pbinom to find the p-value for this problem.
b. Create a confidence interval for the success probability p by inverting the hypothesis test
(namely, the confidence interval contains all po so that you do not reject Ho; for code
implementation, discretize the candidate po E [0, 1]). This interval estimate is a more
reasonable assessment of the reliablity than the point estimate.
c. Use binom.test to verify your result in the last part.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F516f1446-211a-46d9-a124-614103a7f612%2Fe4e62072-e153-446e-87a2-1228ac9ed8f9%2Fdb9uek9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let p be the probability that your printer operates successfully for a job, and suppose that the
operation is independent across jobs. You have printed 20 jobs in a day, and all are successful.
a. You want to find out how reliable your printer is. The point estimate for the reliability p is just
1, and the standard error is 0. We know a printer cannot always work, so this approach
clearly fails. Instead, test the hypothesis
Họ :p = Po
HA :p > Po
VS
0.92. First write down the formula for calculating
at the 0.05 significance level, where po
the p-value. Then use pbinom to find the p-value for this problem.
b. Create a confidence interval for the success probability p by inverting the hypothesis test
(namely, the confidence interval contains all po so that you do not reject Ho; for code
implementation, discretize the candidate po E [0, 1]). This interval estimate is a more
reasonable assessment of the reliablity than the point estimate.
c. Use binom.test to verify your result in the last part.
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