P-value question

[Troyvdg]

---

Members don't see this ad.

A student runs five experiments and obtains the following p-values for the results: 0.065,0.072,0.084,0.056,0.099. What significance level would ensure that the student rejects the null hypothesis only once?

A. 5%
B. 6% *Answer
C. 7%
D. 8%
E. 9%

could someone break this down for me? Stats and I don't sit well. If the p-value is less than or equal to 5% we reject the null hypothesis (right?). but rejecting it more than once? I can't even figure out what the question is asking.

Thanks!

 

[ReaverOpS]

A significance level of 6% would translate to 0.060 which would allow the student to eliminate only one of the choices, which is 0.056. The rest would not be eliminated. However, if you use a significance level of 5%, then none would be rejected. A significance level of 5% or lower would correlate to rejecting (or not accepting) the null hypothesis, which is that the 5 values the student obtained had occurred solely due to chance/probability.

 

[Troyvdg]

thanks for your response.

just to make sure I understand this, by having a significance level of 6%, that would mean that only one value occurred by chance? which is why it would be eliminated?

 

[ReaverOpS]

No, the 4 values would occur by chance, but the value 0.056 would have occurred due to a mechanism OTHER than chance (e.g. it is possible to always get tails if a coin you flip is not a fair coin. In other words, if you flip a coin and obtained 10 tails in a row, and let's say that you obtain a value of 0.032 with a significance level of 5%, then you can reject the null hypothesis (the null hypothesis is that the coin is fair)). Chance/probability is random, which is normal and expected to some degree as long as you obtain p-values greater than your significance level.

 

[PointEstimate]

The definition of P-value is the probability that you obtain a test statistic that is as extreme (or more extreme) than your observation IF the null hypothesis is true. Anything lower the pre-determined level of significance would lead us to reject the null hypothesis.

For example, if we say that our significance level is alpha = 0.05, we are saying that what we observed cannot happen more than 5% of the time when the null hypothesis is true. If we set alpha = 0.01, we are saying that we need even more evidence against our null hypothesis.

Remember, the null hypothesis is one we cannot prove. Rather, we either reject or fail to reject this hypothesis.