1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
FinnZ [79.3K]
3 years ago
8

An automobile manufacturer is considering using robots for part of its assembly process. Converting to robots is an expensive pr

ocess, 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 testH_0: p=0.02 versus H_a: p<.02orH_0: p=0.02 versus H_a: p>.02Explain your answer.b. In the context of this exercise, describe Type I and Type II errors. c. Would you prefer a test with α= .01 or α= .1? Explain your reasoning.
Mathematics
1 answer:
LenKa [72]3 years ago
3 0

Answer:

(a) The correct option is: <em>H₀</em>: <em>p</em> = 0.02 vs. <em>Hₐ</em>: <em>p</em> < 0.02.

(b) Explained below.

(c) The better value of <em>α</em> will be 0.10.

Step-by-step explanation:

An automobile manufacturer is considering using robots for part of its assembly process only if there is strong evidence that the proportion of defective installations is less for the robots than for human assemblers.

To test whether the proportion of defective installations is less for the robots than for human assemblers use a single-proportion <em>z</em>-test.

(a)

The hypothesis can be defined as:

<em>H₀</em>: The proportion of defective installations is same for both the robots and  human assemblers, i.e. <em>p</em> = 0.02.

<em>Hₐ</em>: The proportion of defective installations is less for the robots than for human assemblers, i.e. <em>p</em> < 0.02.

The alternate hypothesis is the claim or the statement that is being tested.

In this case we need to test whether the proportion of defective installations is less for the robots than for human assemblers or not, so that the manufacturer can decide whether they want to apply the conversion.

Thus, the correct option is:

<em>H₀</em>: <em>p</em> = 0.02 vs. <em>Hₐ</em>: <em>p</em> < 0.02.

(b)

A type I error occurs when we discard a true null hypothesis and a type II error is made when we fail to discard a false null hypothesis.

In this case a type I error will be committed if conclude that the proportion of defective installations is less for the robots than for human assemblers when in fact it is not.

And a type II error will be committed if we fail to conclude that proportion of defective installations is less for the robots than for human assemblers.

(c)

The power of the test is the probability of rejecting a false null hypothesis.

The power of the test sis affected by the significance level of the test (<em>α</em>).

Lesser the significance level of the test the lesser is the power of the test.

If the value of <em>α</em> is reduced from 0.05 to 0.01 then the region of acceptance will increase. This implies that there is low probability of rejecting the null hypothesis even when it is false.

So higher the value of <em>α</em> the higher is the probability of making a correct decision.

Thus, the better value of <em>α</em> will be 0.10.

You might be interested in
Put the numbers from least to greatest<br> 3.55<br> 3.544<br> 3.554
nataly862011 [7]

Answer:

3.544 < 3.55 < 3.554

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
What is 555.555 rounded to the nearest 100
koban [17]
600 is the answer to the question
7 0
3 years ago
Read 2 more answers
There has been a person on here posting the same link to many answers, can you please delete their account? Thanks.
klio [65]

Yeah... they should.

4 0
3 years ago
Line k is parallel to y= -2x - 1 and passes through the point (4,3). What is the y intercept of line k?
Schach [20]
Yk what all above you can’t go wrong with choosing all of the em tbh cuz u would get one of them righ
4 0
2 years ago
In every right triangle there is exactly one ____.
bogdanovich [222]

Answer:

point

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Other questions:
  • Rewrite in simplest terms: -7(2u-6v)-7v-3(10v+u)
    15·1 answer
  • Jennifer cut a length of rope into two pieces. One piece was 2 feet 9 inches long, and the other piece was 3 feet 5 inches long.
    14·1 answer
  • Alana praticed dancing for 11 over 4 hours on Monday, 19 over 8 hours on Wednesday, and 2.6 hours on Friday. On which day did sh
    11·1 answer
  • Please give me the answer ASAP The average of 5 numbers is 7. If one of the five numbers is removed, the average of the four rem
    9·2 answers
  • Write an equation of the line that is perpendicular to the line y = 0.5x+8 that passes through the point (4,6)
    7·1 answer
  • Do you know this ?!?!!??!?!!!!!?!?
    12·1 answer
  • New car owners were asked to evaluate their experiences in buying a new car during the past 12 months. In the survey, the owners
    14·2 answers
  • 3
    12·1 answer
  • Please solve this i need this answer ​
    8·2 answers
  • 2x+7=16<br> as a improper fraction simplified
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!