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Draw conclusions based on significance levels and P-values.

Authored by Mr. Kent

Mathematics

12th Grade - University

CCSS covered

Used 10+ times

Draw conclusions based on significance levels and P-values.
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18 questions

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1.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

True or False??

A very high​ P-value is strong evidence that the null hypothesis is false.

This statement is false because a very high​ P-value is strong evidence that the null hypothesis is true.

This statement is true.

This statement is false because a very high​ P-value proves that the null hypothesis is false.

This statement is false because it is a low​ P-value that provides evidence that the null hypothesis is false.

2.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

True or False??

A very low​ P-value proves that the null hypothesis is false.

This statement is true.

This statement is false because a very low​ P-value only shows strong evidence that the null hypothesis is false.

This statement is false because a very low​ P-value proves that the null hypothesis is true.

This statement is false because it is a very high​ P-value that proves that the null hypothesis is false.

3.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

True or False??

A high​ P-value shows that the null hypothesis is true.

This statement is false because a high​ P-value shows that the null hypothesis is false.

This statement is true.

This statement is false because a high​ P-value shows that the data is not consistent with the null​ hypothesis, and can only prove that the null hypothesis is false.

This statement is false because a high​ P-value shows that the data is consistent with the null​ hypothesis, but can never prove that the null hypothesis is true.

4.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

True or False??

A​ P-value below 0.05 is always considered sufficient evidence to reject a null hypothesis.

This statement is false because the null hypothesis is rejected whenever the​ P-value is below the value of α​, which may not necessarily be 0.05.

This statement is false because a​ P-value below 0.05 proves that the null hypothesis is​ false, which is a much stronger result than simply rejecting the null hypothesis.

This statement is true.

This statement is false because it is a​ P-value that is above 0.05 which is always considered sufficient evidence to reject a null hypothesis.

5.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

A medical researcher tested a new treatment for poison ivy against the traditional ointment. He concluded that the new treatment is more effective. Explain what the​ P-value of 0.015 means in this context.

If there is no difference in​ effectiveness, the chance of seeing an observed difference this large or larger is 1.5​% by natural sampling variation.

There is a 1.5​% difference between the effectiveness of the new treatment and the effectiveness of the traditional ointment.

There is a 1.5​% chance that the new treatment is effective.

If there is a difference in​ effectiveness, the chance of seeing an observed difference this large or larger is 1.5​% by natural sampling variation.

6.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Have harsher penalties and ad campaigns increased​ seat-belt use among drivers and​ passengers? Observations of commuter traffic have failed to find evidence of a significant change compared with three years ago. Explain what the​ study's P-value of 0.45 means in this context.

The​ P-value 0.45 is the probability of getting results like the ones obtained in the study by natural variation​ alone, assuming that the proportion of commuters who wear seat belts has increased.

One minus the​ P-value, or 0.55​, is the probability that the proportion of commuters who wear seat belts has changed.

The​ P-value 0.45 is the probability that the proportion of commuters who wear seat belts has changed.

The​ P-value 0.45 is the probability of getting results like the ones obtained in the study by natural variation​ alone, assuming that the proportion of commuters who wear seat belts has not changed.

The​ P-value 0.45 is the probability that the proportion of commuters who wear seat belts has not changed.

7.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

A researcher developing scanners to search for hidden weapons at airports has failed to conclude that a new scanner is significantly better than the current scanner. He made his decision based on a test using α=0.025. Would he have made the same decision at α=0.10? How about α=0.005? Explain. Select the statement relating decision making to values of α.

His decision would have been the same for both α=0.005 and α=0.10.

His decision may have been different for α=0.10 but would have been the same for α=0.005.

His decision may have been different for α=0.005 but would have been the same for α=0.10.

His decision may have been different for both α=0.005 and α=0.10.

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