A manufacturer of hand-held calculators receives large shipments of printed circuits from a supplier. It is too costly and time-consuming to inspect all incoming circuits, so when each shipment arrives, a sample is selected for inspection. Information from the sample is then used to test H0: p = 0.01 versus Ha: p > 0.01, where p is the actual proportion of defective circuits in the shipment. If the null hypothesis is not rejected, the shipment is accepted, and the circuits are used in the production of calculators. If the null hypothesis is rejected, the entire shipment is returned to the supplier because of inferior quality. (A shipment is defined to be of inferior quality if it contains more than 1% defective circuits.) In this context, define Type I and Type II errors. (Select all that apply.) a. A Type I error is obtaining convincing evidence that more than 1% of a shipment is defective when in fact (at most) 1% of the shipment is defective. b. A Type I error is not obtaining convincing evidence that more than 1% of a shipment is defective when in fact more than 1% of the shipment is defective. c. A Type II error is not obtaining convincing evidence that more than 1% of a shipment is defective when in fact more than 1% of the shipment is defective. d. A Type II error is obtaining convincing evidence that more than 1% of a shipment is defective when in fact (at most) 1% of the shipment is defective.

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Description: A manufacturer of hand-held calculators receives large shipments of printed circuits from a supplier. It is too costly and time-consuming to inspect all incoming circuits, so when each shipment arrives, a sample is selected for inspection. Informatio

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

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A manufacturer of hand-held calculators receives large shipments of printed circuits from a supplier. It is too costly and time-consuming to inspect all incoming circuits, so when each shipment arrives, a sample is selected for inspection. Information from the sample is then used to test

H₀: p = 0.01

versus

H_a: p > 0.01,

where p is the actual proportion of defective circuits in the shipment.

If the null hypothesis is not rejected, the shipment is accepted, and the circuits are used in the production of calculators. If the null hypothesis is rejected, the entire shipment is returned to the supplier because of inferior quality. (A shipment is defined to be of inferior quality if it contains more than 1% defective circuits.)

In this context, define Type I and Type II errors. (Select all that apply.)

a. A Type I error is obtaining convincing evidence that more than 1% of a shipment is defective when in fact (at most) 1% of the shipment is defective.

b. A Type I error is not obtaining convincing evidence that more than 1% of a shipment is defective when in fact more than 1% of the shipment is defective.

c. A Type II error is not obtaining convincing evidence that more than 1% of a shipment is defective when in fact more than 1% of the shipment is defective.

d. A Type II error is obtaining convincing evidence that more than 1% of a shipment is defective when in fact (at most) 1% of the shipment is defective.

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