What can be deduced from the following hypothesis test given the $p$ value? You want to find out whether a new medicine for flu is effective or not. You know that the general assumption is that an average flu last for about one
week. So, letting $t$ be the average disease duration, you formulate your null hypothesis as $H_0: t \geq 7$ vs. $H_1: t < 7$. Your test result returned a $p$ value of $0.05$.
Which of the following statements are correct?

*

*After treatment with the new drug there is a 95% chance that a flu    will last less than 7 days.

*In 95% of the cases, the flu will last less than 7 days.

*The duration of the flu can be reduced by a factor of 0.05%.

*Even if the new medicine was completely ineffective, the chances that the experiment would have produced the same result are 0.05%.

*We have proven that the null-hypothesis H0 is wrong and your    medicine is effective.

Since the $p$ value is small we will reject the null hypothesis which is on an avg flu lasts more than or equal to 7 days. By that answer 1 is CORRECT and answer 5 as well. What about the rest? How do I decide that?
P.S this is the first time I touching stats. Please help!
 A: None of the options provided are true. This might be an example of the fairly common disease of statistics instructors not understanding p-values. Many other examples can be found. See this paper: https://bpspubs.onlinelibrary.wiley.com/doi/full/10.1111/j.1476-5381.2012.01931.x
Also Haller & Krause (2002).
For a significance test, what you know from the p-value of 0.05 is that there is pretty weak statistical evidence suggesting that the null hypothesis is false. For a hypothesis test your decision to reject the null or not would depend on whether your pre-defined critical cutoff (rejection region) was greater or less than 0.05. If you used the convention of p<0.05 as the cutoff then your result of p=0.05 would give the opposite decision from what you would get if you set the cutoff to p≤0.05!
Haller H, Krauss S (2002). Misinterpretations of significance: a problem students share with their teachers. Methods Psychol Res 7: 1–20.
A: As @MichaelLew said,none of the answers is 100% true. The question and answers are poorly worded.

*

*Answer 1 is about the distribution of flu duration among people. The study is only about average length and you have no information about the distribution among different people.


*Answer 2 is also about the distribution of flu duration among people, just asking it differently. Nothing in the problem gives a clue about the distribution.


*Answer 3 is about relative duration of flu. Nothing in the problem gives you information about the durations or the relative duration.


*Answer 4 is wrong because of "same result". P value is about same result or even more extreme result (or same or more extreme difference in the other direction, if two-sided p-value). Moreover, answer 4 incorrectly equates a probability of 0.05 with 0.05% (rather than 5%).


*Answer 5 says "proven". Statistics can never absolutely prove in one study. Statistics is about probabilities.
As written therefore, all answers are wrong. But #4 the closest to being correct.
