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The level of significance is the probability that a true hypothesis is rejected. TRUE

The level of significance is represented as a p-value and called alpha. If we get a p-value of .05, the probability of saying there is a difference when one DOES NOT exist is 5%--an alpha of .05.  If we say there is a difference but one doesn't really exist, the we've committed a Type I error. In other words our significance level is the probability of accepting the alternative hypothesis when it is not true. 
This is a terribly worded question since I believe by "true hypothesis" they are refering to the NULL hypothesis. We don't typically refer to the NULL hypothesis as a "true" hypothesis, its more the default state. When we fail to reject the NULL, it doesn't necessaarily mean it is true, it often just means we have insufficient evidence to reject it--which is different than saying its true.

A Type one error is also referred to as an alpha risk: TRUE
As explained in the first part, a Type I error is reflected in the alpha and p-value.

For a one-tailed test of Hypothesis, the area of rejection is only in one tail of the test. TRUE
As the name suggests, 1-tailed areas use only one tail to generate the p-value or rejection (of the null hypothesis) region.

The level of significance is selected after setting up a decision rule. FALSE
You'd typically setup the level of significance first. So you'd say, we'll reject the null hypothesis if the probability of a Type I error is less than .05. You then find the critical value from the distribution (say the t or z) based on the level of significance and sample size. If you test statistic is above (or below depending on the direction of the test) then you'd decided to reject or not reject the Null Hypothesis.

To set up a decision rule, the sampling distribution is divided into two regions a region of non-rejection and a region where the null hypothesis is rejected. TRUE
With your critical value chosen based on your significance level and whether it is a 1 or 2 sided test, you will have two regions--one where you reject the null and one where you fail to reject the null hypothesis

There is no one level of significance that is applied to all studies involving sampling. TRUE
While it is common to use p <.05 as the significance level for many studies it does not always need to be this way and can vary to .01, .10, .15 etc. This always depends on context or what the price is for being wrong.

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