Draw conclusions based on significance levels and P-values.

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.

Which of the following is the FIRST step of a hypothesis test?

• Check assumptions & conditions
• Find your test statistic
• State your conclusion
• State your null & alternative hypotheses