What is the level of significance?
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A. B. C. D. E.E
The level of significance and the type I error are both the probability of rejecting the null hypothesis when it is actually true.
The correct answer to the question "What is the level of significance?" is E. Probability of a Type I error.
The level of significance, also known as alpha (α), is a predetermined threshold used in hypothesis testing to determine the likelihood of rejecting a null hypothesis when it is actually true. It represents the maximum probability of making a Type I error, which is the rejection of a null hypothesis when it is true.
In hypothesis testing, the null hypothesis (H0) represents the default assumption or the claim being tested, while the alternative hypothesis (Ha) is the claim that is being considered as an alternative to the null hypothesis. The level of significance helps determine whether there is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.
To conduct hypothesis testing, a significance level is chosen before conducting the test. Common levels of significance include 0.05 (5%) and 0.01 (1%). These values represent the maximum allowable probability of making a Type I error.
A Type I error occurs when the null hypothesis is rejected, even though it is true. In other words, it is a false positive result. The probability of committing a Type I error is directly related to the chosen level of significance. For example, if a 5% significance level (0.05) is selected, it means that there is a 5% chance of rejecting the null hypothesis when it is actually true.
In the given answer choices: A. None of these answers: This is incorrect as one of the options must be the correct answer. B. Probability of a Type II error: This is incorrect. The level of significance is not directly related to the probability of a Type II error. The probability of a Type II error is denoted by beta (β) and represents the likelihood of failing to reject a false null hypothesis. C. Beta error: This is incorrect. Beta error is the probability of a Type II error and is not related to the level of significance. D. Z-value of 1.96: This is incorrect. The Z-value of 1.96 corresponds to a critical value for a 95% confidence level in a standard normal distribution, but it is not the level of significance. E. Probability of a Type I error: This is the correct answer. The level of significance is directly related to the probability of a Type I error, representing the maximum allowable probability of rejecting a true null hypothesis.
Therefore, the correct answer is E. Probability of a Type I error.