Limits of confidence of a hypothesis determined by?
**Core Concept**
The concept being tested here is related to hypothesis testing in statistics, specifically the relationship between the level of significance and the limits of confidence. In hypothesis testing, the level of significance (α) is the maximum probability of rejecting the null hypothesis when it is true, while the limits of confidence refer to the range within which the true population parameter is likely to lie.
**Why the Correct Answer is Right**
The correct answer, **1 -level of significance**, is based on the relationship between the level of significance (α) and the confidence level (1 - α). The confidence level is the probability that the interval estimate will contain the true population parameter. In other words, it is the probability that the null hypothesis will not be rejected when it is true. When the level of significance is set at α, the confidence level is 1 - α. This means that if the null hypothesis is true, there is a 1 - α probability that the interval estimate will contain the true population parameter.
**Why Each Wrong Option is Incorrect**
**Option A:** The power factor is not directly related to the limits of confidence. Power is the probability of rejecting the null hypothesis when it is false.
**Option B:** The level of significance (α) is the maximum probability of rejecting the null hypothesis when it is true, but it does not determine the limits of confidence.
**Option C:** 1 - power factor is not a correct expression for the limits of confidence. Power is the probability of rejecting the null hypothesis when it is false.
**Clinical Pearl / High-Yield Fact**
When conducting hypothesis testing, it's essential to understand the relationship between the level of significance and the confidence level. A higher level of significance (α) leads to a lower confidence level (1 - α), and vice versa. This is a critical concept in statistical inference, and students should be familiar with it to accurately interpret the results of hypothesis tests.
**✓ Correct Answer: D. 1 -level of significance**