An automobile manufacturer is considering using robots for part of its assembly process. Converting to robots is an expensive process, so it will be undertaken only if there is strong evidence that the proportion of defective installations is less for the robots than for human assemblers. Let p denote the actual proportion of defective installations for the robots. It is known that the proportion of defective installations for human assemblers is 0.02. (a) Which of the following pairs of hypotheses should the manufacturer test? H0: p = 0.02 versus Ha: p < 0.02 or H0: p = 0.02 versus Ha: p > 0.02 Explain your answer. H0: p = 0.02 versus Ha: p < 0.02, as the conversion will only happen if the proportion of defective installations is higher for robots.H0: p = 0.02 versus Ha: p < 0.02, as the conversion will only happen if the proportion of defective installations is lower for robots. H0: p = 0.02 versus Ha: p > 0.02, as the conversion will only happen if the proportion of defective installations is higher for robots.H0: p = 0.02 versus Ha: p > 0.02, as the conversion will only happen if the proportion of defective installations is lower for human assemblers. (b) In the context of this exercise, describe Type I and Type II errors. (Select all that apply.) A Type I error would be not obtaining convincing evidence that the proportion of defective installations for the robots is less than 0.02 when in fact it is less than 0.02.A Type II error would be not obtaining convincing evidence that the proportion of defective installations for the robots is less than 0.02 when in fact it is less than 0.02.A Type II error would be obtaining convincing evidence that the proportion of defective installations for the robots is less than 0.02 when in fact it is (at least) 0.02.A Type I error would be obtaining convincing evidence that the proportion of defective installations for the robots is less than 0.02 when in fact it is (at least) 0.02. (c) Would you prefer a test with ? = 0.01 or ? = 0.1? Explain your reasoning. 0.01, as a Type I error results in people losing their jobs to a robot system that doesn't improve accuracy.0.1, as a Type I error results in people losing their jobs to a robot system that doesn't improve accuracy. 0.01, as a Type II error results in people losing their jobs to a robot system that doesn't improve accuracy.0.1, as a Type II error results in people losing their jobs to a robot system that doesn't improve accuracy.

An automobile manufacturer is considering using robots for part of its assembly process. Converting to robots is an expensive process, so it will be undertaken only if there is strong evidence that the proportion of defective installations is less for the robots than for human assemblers. Let p denote the actual proportion of defective installations for the robots. It is known that the proportion of defective installations for human assemblers is 0.02. (a) Which of the following pairs of hypotheses should the manufacturer test? H0: p = 0.02 versus Ha: p < 0.02 or H0: p = 0.02 versus Ha: p > 0.02 Explain your answer. H0: p = 0.02 versus Ha: p < 0.02, as the conversion will only happen if the proportion of defective installations is higher for robots.H0: p = 0.02 versus Ha: p < 0.02, as the conversion will only happen if the proportion of defective installations is lower for robots. H0: p = 0.02 versus Ha: p > 0.02, as the conversion will only happen if the proportion of defective installations is higher for robots.H0: p = 0.02 versus Ha: p > 0.02, as the conversion will only happen if the proportion of defective installations is lower for human assemblers. (b) In the context of this exercise, describe Type I and Type II errors. (Select all that apply.) A Type I error would be not obtaining convincing evidence that the proportion of defective installations for the robots is less than 0.02 when in fact it is less than 0.02.A Type II error would be not obtaining convincing evidence that the proportion of defective installations for the robots is less than 0.02 when in fact it is less than 0.02.A Type II error would be obtaining convincing evidence that the proportion of defective installations for the robots is less than 0.02 when in fact it is (at least) 0.02.A Type I error would be obtaining convincing evidence that the proportion of defective installations for the robots is less than 0.02 when in fact it is (at least) 0.02. (c) Would you prefer a test with ? = 0.01 or ? = 0.1? Explain your reasoning. 0.01, as a Type I error results in people losing their jobs to a robot system that doesn't improve accuracy.0.1, as a Type I error results in people losing their jobs to a robot system that doesn't improve accuracy. 0.01, as a Type II error results in people losing their jobs to a robot system that doesn't improve accuracy.0.1, as a Type II error results in people losing their jobs to a robot system that doesn't improve accuracy.

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Description: An automobile manufacturer is considering using robots for part of its assembly process. Converting to robots is an expensive process, so it will be undertaken only if there is strong evidence that the proportion of defective installations is less fo

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

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(a)

Which of the following pairs of hypotheses should the manufacturer test?

H₀: p = 0.02 versus H_a: p < 0.02

H₀: p = 0.02 versus H_a: p > 0.02

Explain your answer.

H₀: p = 0.02 versus H_a: p < 0.02, as the conversion will only happen if the proportion of defective installations is higher for robots.H₀: p = 0.02 versus H_a: p < 0.02, as the conversion will only happen if the proportion of defective installations is lower for robots. H₀: p = 0.02 versus H_a: p > 0.02, as the conversion will only happen if the proportion of defective installations is higher for robots.H₀: p = 0.02 versus H_a: p > 0.02, as the conversion will only happen if the proportion of defective installations is lower for human assemblers.

(b)

In the context of this exercise, describe Type I and Type II errors. (Select all that apply.)

A Type I error would be not obtaining convincing evidence that the proportion of defective installations for the robots is less than 0.02 when in fact it is less than 0.02.A Type II error would be not obtaining convincing evidence that the proportion of defective installations for the robots is less than 0.02 when in fact it is less than 0.02.A Type II error would be obtaining convincing evidence that the proportion of defective installations for the robots is less than 0.02 when in fact it is (at least) 0.02.A Type I error would be obtaining convincing evidence that the proportion of defective installations for the robots is less than 0.02 when in fact it is (at least) 0.02.

(c)

Would you prefer a test with ? = 0.01 or ? = 0.1? Explain your reasoning.

0.01, as a Type I error results in people losing their jobs to a robot system that doesn't improve accuracy.0.1, as a Type I error results in people losing their jobs to a robot system that doesn't improve accuracy. 0.01, as a Type II error results in people losing their jobs to a robot system that doesn't improve accuracy.0.1, as a Type II error results in people losing their jobs to a robot system that doesn't improve accuracy.

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