Production managers on an assembly line must monitor the output to be sure that the level of defective products remains small. They periodically inspect a random sample of the items produced. If they find a significant increase in the proportion of items that must be rejected, they will halt the assembly process until the problem can be identified and repaired.

a. In this context, what is a Type I error?
b. In this context, what is a Type II error?
c. Which type of error would the factory owner consider more serious?
d. Which type of error might customers consider more serious?

Question

04-02-2020
Mathematics

contestada

Production managers on an assembly line must monitor the output to be sure that the level of defective products remains small. They periodically inspect a random sample of the items produced. If they find a significant increase in the proportion of items that must be rejected, they will halt the assembly process until the problem can be identified and repaired.

a. In this context, what is a Type I error?
b. In this context, what is a Type II error?
c. Which type of error would the factory owner consider more serious?
d. Which type of error might customers consider more serious?

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Alcaa Alcaa · Answer 1 · 2020-02-04T09:06:48+01:00

Answer:

(a) Type I error in our context is that our test indicates that the proportion of defective products has increased after inspecting but in actual the proportion of defective products was small.

(b) Type II error in our context is that our test indicates that the proportion of defective products has remained small after inspecting but in actual the proportion of defective products was increased.

(c) Factory owner would consider Type 1 error more serious.

(d) Customers will consider Type II error more serious.

Step-by-step explanation:

Let [tex]H_0[/tex] = Proportion of defective products remains small

[tex]H_1[/tex] = Proportion of defective products increases

(a) Type I error represents that we have rejected our null hypothesis given the fact that null hypothesis is True.

Interpretation of this Type I error in our context is that our test indicates that the proportion of defective products has increased after inspecting but in actual the proportion of defective products was small.

(b) Type II error represents that we have accepted our null hypothesis given the fact that null hypothesis is False.

Interpretation of this Type II error in our context is that our test indicates that the proportion of defective products has remained small after inspecting but in actual the proportion of defective products was increased.

(c) Factory owner would consider Type 1 error more serious because after inspecting and testing he assumed that the proportion of defective products has increased due to which he will halt the assembly process till the time the problem is identified and is repaired but in actual he should continue his assembly process as in actual the proportion of defective products was small.

(d) Customers will consider Type II error more serious because after inspecting and testing factory owner assumed that the proportion of defective products is small and he will keeps on producing products and assembly process will keeps on going but in actual the proportion of defective products was increased and due to which customers will not get good quality products and they will not be able to purchase the products further.