
significance test
The pvalue of a twotailed ztest for a population mean is 0.064 when the level of significance is 0.05. Which of the following statements are true?
 I. A onesided test using the same data would indicate a statistically significant result.
II. The mean in the null hypothesis is true.
 III. The test has failed to prove that the alternative hypothesis is true
I and III are correct but I have couple questions.
1) When dealing with two sided tests, significance levels(alpha) are halfed just like Pvalues
2)What does it really mean by "statistically significant result" ? I tried googling but couldn't find a good answer.
Thanks for your help in advance.

Question (1) isn't a question. It's a statement. Unless you meant for it to have a question mark on the end. If so, the reason pvalues are halved, is because you are looking for the chance that you will get a maximum, and a minimum value away from the mean  i.e., what are the chances you will get a value Xnumber of standard deviations above and below the mean. That probability is contained in to halves of the curve. Thus, we split the TOTAL pvalue in half.
Question (2) is going to get a long answer. If a result is "statistically significant" it means the result you observed, is unlikely to have occurred by chance. Here is a little experiment:
Say the mean ounce in some drink is reported to be 16 ounces, with a standard deviation of 0.5 ounces. You get a drink and find that the case of soda you have, has a mean ounce of 14.25 ounces. You exclaim  "I'm being shorted!" You conduct a hypothesis test that the mean number of ounces in the soda is less than 16, with a 0.05 level of significance and find that your test statistic lies in the rejection region, with a pvalue (I'm making this up) of lets say 0.02. What this means, is that IF the mean ounces in a soda can WERE 16ounces (or in general if the null hypothesis WERE true), you would have a 2% "chance" of getting a case of soda that had an average ounceage of 14.25 or less. Is it impossible? Of course not. Is it unlikely. Probably. Therefore, at a 0.05 level of significant, you would reject the notion that the mean ounces in a soda is 16.
Some people do not like reporting the level of significance, and instead rely on the pvalue. The pvalue tells you oh so much more than a siglevel: the pvalue is LITERALLY the probability of getting the value you observed (14.25)  or something more extreme than that (usually its worded as " the pvalue is the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true"  which always confused me until I took the time to sit down and really read my textbook). I like the pvalue because it is what you have been dealing with up to the point  area under a curve. All of a sudden we then toss siglevels at you; I suppose for the general public, pvalues are less easier to understand than confidence levels, but a pvalue has more intuitive information in it.