As a statistical expert with extensive experience in data analysis and hypothesis testing, I often encounter the concept of significance levels in the context of statistical inference. The term ".05 level of significance" is a fundamental concept in hypothesis testing and it refers to the probability threshold that researchers use to determine whether to reject the null hypothesis in favor of the alternative hypothesis.

In statistical hypothesis testing, we start with a null hypothesis (H0) which represents a default assumption that there is no effect or no difference between the groups being studied. The alternative hypothesis (H1 or Ha), on the other hand, is what the researcher is interested in proving; it represents the claim that there is an effect or a difference.

The significance level, often denoted by the Greek letter alpha (α), is a pre-determined threshold that is used to make a decision about the null hypothesis. It is the probability of rejecting the null hypothesis when it is actually true, which is also known as a Type I error. The significance level is chosen by the researcher before the study begins and is typically set at a value that reflects the seriousness of making a Type I error. Commonly used significance levels include 0.05, 0.01, and 0.001.

When conducting a hypothesis test, statisticians calculate a test statistic, which is then compared to a critical value derived from the significance level. If the test statistic is more extreme than the critical value (or if the calculated p-value is less than the significance level), the null hypothesis is rejected in favor of the alternative hypothesis. The p-value is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from the data, assuming the null hypothesis is true.

Setting the significance level at .05 means that there is a 5% chance of committing a Type I error if the null hypothesis is true. This level is a balance between being too conservative (which would mean rarely rejecting a true null hypothesis and thus missing out on potentially important findings) and being too liberal (which would mean frequently rejecting true null hypotheses and thus accepting false findings).

It's important to note that the significance level is not a measure of the strength of the evidence against the null hypothesis, nor is it the probability that the null hypothesis is true. It is simply the threshold that has been set to make a decision about the null hypothesis.

In summary, a .05 level of significance is a threshold used in hypothesis testing to determine the likelihood of rejecting the null hypothesis when it is true. It is a critical concept in statistical analysis that helps researchers make informed decisions about their data and the validity of their findings.

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The null hypothesis is rejected if the p-value is less than a predetermined level, --. -- is called the significance level, and is the probability of rejecting the null hypothesis given that it is true (a type I error). It is usually set at or below 5%.read more >>