To find the critical z score value for a 90% confidence level, we first need to understand what that means in the context of a standard normal distribution.
A 90% confidence level means that we expect our true parameter (like a population mean) to lie within the interval we calculate 90% of the time. This implies that 5% of the distribution will fall in each tail (the lower and upper), leaving us with the central 90%.
To find the critical z score, we look for the z value that corresponds to a cumulative area of 0.95 (since we want the central 90%, and the upper 5% corresponds to the 95th percentile). Using a standard normal distribution table or a calculator:
- Find the z value that gives an area of 0.95.
- This value is approximately 1.645.
Therefore, the critical z score value for the 90% confidence level is approximately 1.645.
In practice, this means that if you are working with a sample mean and want to create a 90% confidence interval, you would use this z score to calculate the margin of error from the sample mean.