WorksheetsDraw conclusions based on significance levels and P-values.
Total questions: 18
Worksheet time: 2hrs 30mins
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.
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.
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.
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.
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.
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.
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.
Public health officials believe that 90.5% of children have been vaccinated against measles. A random survey of medical records at many schools across the country found that, among more than 13,000 children, only 88.5% had been vaccinated. A statistician would reject the 90% hypothesis with a P-value of P=0.006.
There is only a 0.6% chance that 90.5% is the actual percentage of vaccinated children.
There is only a 0.6% chance that 90.5% is not the actual percentage of children vaccinated.
There is only a 0.6% chance that a sample proportion of 88.5% is statistically different from the reported 90.5% of children vaccinated
There is only a 0.6% chance of seeing a sample proportion as low as 88.5% vaccinated by natural sampling variation if 90.5% have really been vaccinated.
A pharmaceutical company investigating whether drug stores are less likely than food stores to remove over-the-counter drugs from the shelves when the drugs are past the expiration date found a P-value of 2.8%. What does this mean?
None of these
2.8% more drug stores remove over-the-counter drugs from the shelves when the drugs are past the expiration date.
There is a 97.2% chance the drug stores remove more expired over-the-counter drugs.
97.2% more drug stores remove over-the-counter drugs from the shelves when the drugs are past the expiration date than food stores.
A P-value indicates:
the probability that the null hypothesis is true
the probability that the alternative hypothesis is true
the probability of the observed results given the null hypothesis is false
the probability that the null is true given the observed results
Suppose the P-value for a hypothesis test is 0.0304. Using a = 0.05, what is the appropriate conclusion?
a) reject the null, the probability of getting results like this given the null is true is 3.04% which is less than 5%.
b) reject the alternative, the probability of getting results like this given the alternative is true is 3.04% which is less than 5%.
c) Accept the null, a 3.04% chance is really not that bad.
d) Fail to reject the alternative but still don't accept the null.
Significance Level: 10%
Significance Level: 10%
True or False??
The z statistic is how many standard deviations above or below the mean of the sampling distribution is from the sample proportion.
True!
False!
Who cares! The z statistic makes me zzzzzzzz........
Which of the following is a correct interpretation of a P-value that is not very small?
What we saw in the sample data is not surprising, so we fail to reject the null hypothesis.
We have witnessed a rare event, so we should reject the null hypothesis.
What we saw in the sample data is not surprising, so we reject the null hypothesis.
We have witnessed a rare event, so we should fail to reject the null hypothesis.
If the P-value is smaller than the level of significance, what conclusion should we reach?
Reject the null hypothesis.
Accept the null hypothesis as true.
Fail to reject the null hypothesis.
We should cry.
