To find the value of Z subscript alpha divided by 2 that corresponds to a confidence level of 0.8948, we follow these steps:
- Understand the Confidence Level: The confidence level of 0.8948 means that we are looking for the Z-score that leaves 0.8948 of the area under the standard normal curve.
- Determine Alpha: The significance level (alpha) is calculated as 1 minus the confidence level. In this case, alpha = 1 – 0.8948 = 0.1052.
- Divide Alpha by 2: Since we want to find Z subscript alpha divided by 2, we take 0.1052 and divide it by 2, giving us 0.0526.
- Use Z-Score Tables or Calculator: We now need to look for the Z-score that corresponds to the cumulative area of 0.0526. Typically, we look for the Z-score that gives an area to the left of it equal to 0.0526, which corresponds to approximately -1.96 (considering the negative Z-score for the left tail).
- Final Value: Therefore, Z subscript alpha divided by 2, corresponding to a confidence level of 0.8948, is -1.96.
This Z-score can also be confirmed using statistical software or a standard normal distribution calculator. It is essential for interpreting statistical results, particularly in constructing confidence intervals.