To calculate the Level of Significance (p-value):
\[ \text{p-value} = 1 - Z(\text{ABS}(z)) \]
Where:
A level of significance is a statistical term that represents the probability of rejecting a null hypothesis when it is true. It is often denoted by the Greek letter alpha (α) and is used to determine the threshold for rejecting the null hypothesis. The level of significance is typically set at 0.05, which means there is a 5% risk of concluding that a difference exists when there is no actual difference. Lowering the level of significance reduces the chances of making a Type I error (false positive), but increases the chances of making a Type II error (false negative).
Let's assume the following value:
Using the formula:
\[ \text{p-value} = 1 - Z(\text{ABS}(1.96)) = 1 - 0.975 = 0.025 \]
The p-value is 0.025.
Let's assume the following value:
Using the formula:
\[ \text{p-value} = 1 - Z(\text{ABS}(2.58)) = 1 - 0.995 = 0.005 \]
The p-value is 0.005.