INSTRUCTIONS: Please provide all the answers. Do not provide INCOMPLETE answer P

Question

INSTRUCTIONS:

Please provide all the answers. Do not provide INCOMPLETE answer

PLEASE REPLY TO THE COMMENT OR CORRECT THE INCOMPLETE ANSWER AFTER YOU POST THE ANSWER.

PLEASE GIVE ACCURATE ANSWERS. THIS IS FOR ALEKS. SO ANSWERS ARE ASSESSED BY COMPUTER SYSTEM.

Question:

Based on this information, answer the questions below. Carry your intermediate computations to at least four decimal places, and round your responses as indicated.

1.

What are the null and alternative hypotheses that the managers should use for the test?

2. What is the probability that the managers commit a Type I error? Round your response to at least two decimal places: _________________

3. Assuming that the actual value of µ is 41.3 minutes, what is the probability that the managers commit a Type II error? Round your response to at least two decimal places: ________________

4. Suppose that the managers decide to perform another statistical test using the same population, the same null and alternative hypotheses, and the same level of significance, but for this second test the managers choose a random sample of size 125 instead of a random sample of size 100. Assuming that the actual value of µ is 41.3 minutes, how does the power of this second test compare to the power of the original test?

(Select one):

(a) The power of the second test is greater than the power of the original test

(b) The power of the second test is less than the power of the original test

(c) The powers of the two tests are equal

(SNAPSHOT):

INSTRUCTIONS:

Please provide all the answers. Do not provide INCOMPLETE answer

PLEASE REPLY TO THE COMMENT OR CORRECT THE INCOMPLETE ANSWER AFTER YOU POST THE ANSWER.

PLEASE GIVE ACCURATE ANSWERS. THIS IS FOR ALEKS. SO ANSWERS ARE ASSESSED BY COMPUTER SYSTEM.

Question:

Managers at an automobile manufacturing plant would like to examine the mean completion time for an assembly line operation. The past data indicate that the mean completion time is minutes , but the managers have reason to believe that this value has decreased. The managers plan to perform a statistical test of the claim and choose a random sample of completion times in preparation for this test.

Suppose that the population of completion times for the assembly line operation has a standard deviation of minutes and that the managers perform their hypothesis test using the level of significance.

Based on this information, answer the questions below. Carry your intermediate computations to at least four decimal places, and round your responses as indicated.

Explanation / Answer

Answer:

H0: µ is greater than or equal to 42

H1: µ is less than 42

Explanation: Here the claim is that the value has decreased so this is left-tailed test.

2. Answer: Type I Error: 0.01

Explanation: Level of significance is nothing but the probability of type I Error.

3. From the level of significance we find that the null hypothesis can be rejected if,

z -1.28 (from normal distribution)

Now x bar = µ + ((s / Ön)*z)) = 42+ ((5/Ö100)*-1.28) = 41.36

Now we need to find P ( x bar > 41.36 )

The z-score = (41.36 – 41.3) / ( 5 / Ö100) = 0.12

Type II Error = P ( z > 0.12 ) = 1 – P ( z < 0.12) = 1 – 0.5478 = 0.4522

Answer: 0.4522

4. Answer: (a) The power of the second test is greater than the power of the original test.

Explanation: We know that for the hypothesis testing the greater the sample size, the greater the power of the test.

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