interval then the null hypothesis can be rejected at the 0.05 ..
Testing at a 5% level of significance means that you only have a 5% chance of rejecting the null hypothesis.
then the null hypothesis can be rejected at the 0.05 level.
Once the type of test is determined, the details of the test must be specified. Specifically, the null and alternative hypotheses must be clearly stated. The null hypothesis always reflects the "no change" or "no difference" situation. The alternative or research hypothesis reflects the investigator's belief. The investigator might hypothesize that a parameter (e.g., a mean, proportion, difference in means or proportions) will increase, will decrease or will be different under specific conditions (sometimes the conditions are different experimental conditions and other times the conditions are simply different groups of participants). Once the hypotheses are specified, data are collected and summarized. The appropriate test is then conducted according to the five step approach. If the test leads to rejection of the null hypothesis, an approximate pvalue is computed to summarize the significance of the findings. When tests of hypothesis are conducted using statistical computing packages, exact pvalues are computed. Because the statistical tables in this textbook are limited, we can only approximate pvalues. If the test fails to reject the null hypothesis, then a weaker concluding statement is made for the following reason.
Here are three experiments to illustrate when the different approaches to statistics are appropriate. In the first experiment, you are testing a plant extract on rabbits to see if it will lower their blood pressure. You already know that the plant extract is a diuretic (makes the rabbits pee more) and you already know that diuretics tend to lower blood pressure, so you think there's a good chance it will work. If it does work, you'll do more lowcost animal tests on it before you do expensive, potentially risky human trials. Your prior expectation is that the null hypothesis (that the plant extract has no effect) has a good chance of being false, and the cost of a false positive is fairly low. So you should do frequentist hypothesis testing, with a significance level of 0.05.
can reject a null hypothesis at the 0.05 level, ..
Now instead of testing 1000 plant extracts, imagine that you are testing just one. If you are testing it to see if it kills beetle larvae, you know (based on everything you know about plant and beetle biology) there's a pretty good chance it will work, so you can be pretty sure that a P value less than 0.05 is a true positive. But if you are testing that one plant extract to see if it grows hair, which you know is very unlikely (based on everything you know about plants and hair), a P value less than 0.05 is almost certainly a false positive. In other words, if you expect that the null hypothesis is probably true, a statistically significant result is probably a false positive. This is sad; the most exciting, amazing, unexpected results in your experiments are probably just your data trying to make you jump to ridiculous conclusions. You should require a much lower P value to reject a null hypothesis that you think is probably true.
Having said that, there's one key concept from Bayesian statistics that is important for all users of statistics to understand. To illustrate it, imagine that you are testing extracts from 1000 different tropical plants, trying to find something that will kill beetle larvae. The reality (which you don't know) is that 500 of the extracts kill beetle larvae, and 500 don't. You do the 1000 experiments and do the 1000 frequentist statistical tests, and you use the traditional significance level of PPPP value, after all), so you have 25 false positives. So you end up with 525 plant extracts that gave you a P value less than 0.05. You'll have to do further experiments to figure out which are the 25 false positives and which are the 500 true positives, but that's not so bad, since you know that most of them will turn out to be true positives.
less than 0.05), we can then reject the null hypothesis.
We reject H_{0} because 2.66 > 1.960. We have statistically significant evidence at α=0.05 to show that there is a difference in mean systolic blood pressures between men and women. The pvalue is p
We rejected the null hypothesis, i.e., claimed that the height is not 65, thus making potentially a Type I error. But sometimes the pvalue is too low because of the large sample size, and we may have statistical significance but not really practical significance! That's why most statisticians are much more comfortable with using CI than tests.
level of significance at which a null hypothesis is rejected.

Null and Alternative Hypothesis  Real Statistics Using Excel
Suppose that in this kind of operation, the traditionally acceptable level of significance has been .05.

Confidence Intervals & Hypothesis Testing (1 of 5)
The pvalue of a test is the smallest level of significance at which the null hypothesis can be rejected

Null Hypothesis Definition  Investopedia
the smallest level of significance at which the null hypothesis can be rejected.
Statistical hypothesis testing  Wikipedia
This criticism only applies to twotailed tests, where the null hypothesis is "Things are exactly the same" and the alternative is "Things are different." Presumably these critics think it would be okay to do a onetailed test with a null hypothesis like "Foot length of male chickens is the same as, or less than, that of females," because the null hypothesis that male chickens have smaller feet than females could be true. So if you're worried about this issue, you could think of a twotailed test, where the null hypothesis is that things are the same, as shorthand for doing two onetailed tests. A significant rejection of the null hypothesis in a twotailed test would then be the equivalent of rejecting one of the two onetailed null hypotheses.
Hypothesis testing  Handbook of Biological Statistics
The power of a statistical test is its probability of rejecting the null hypothesis if the null hypothesis is false. That is, power is the ability to correctly reject H_{0} and detect a significant effect. In other words, power is one minus the type II error risk.
Significance Tests / Hypothesis Testing – Jerry Dallal
A related criticism is that a significant rejection of a null hypothesis might not be biologically meaningful, if the difference is too small to matter. For example, in the chickensex experiment, having a treatment that produced 49.9% male chicks might be significantly different from 50%, but it wouldn't be enough to make farmers want to buy your treatment. These critics say you should estimate the effect size and put a on it, not estimate a P value. So the goal of your chickensex experiment should not be to say "Chocolate gives a proportion of males that is significantly less than 50% (P=0.015)" but to say "Chocolate produced 36.1% males with a 95% confidence interval of 25.9 to 47.4%." For the chickenfeet experiment, you would say something like "The difference between males and females in mean foot size is 2.45 mm, with a confidence interval on the difference of ±1.98 mm."
Significance Tests / Hypothesis Testing
In the olden days, when people looked up P values in printed tables, they would report the results of a statistical test as "PPP>0.10", etc. Nowadays, almost all computer statistics programs give the exact P value resulting from a statistical test, such as P=0.029, and that's what you should report in your publications. You will conclude that the results are either significant or they're not significant; they either reject the null hypothesis (if P is below your predetermined significance level) or don't reject the null hypothesis (if P is above your significance level). But other people will want to know if your results are "strongly" significant (P much less than 0.05), which will give them more confidence in your results than if they were "barely" significant (P=0.043, for example). In addition, other researchers will need the exact P value if they want to combine your results with others into a .