Z0.025 = 1.96 and 0.06
I am assuming the 0.06 is the alpha divided by 2 + 1 since the population variance is known. I've figured out how the .9750 was found, sort of, doesn't really go in depth on that part, but where does the 6 in 1.96 come into play, is it even important? I guess my question is how did you get the z0.025 = 1.96 and not just 1.9
Hi Elijah,
The value of z = 1.96 comes from the properties of the standard normal distribution. It's not related to the number 6 or any other number in the problem you're working on. The reason we use 1.96 in many statistical tests (like a two-tailed test with a significance level of 0.05) is that 1.96 is the z-score that marks off the upper 2.5% of the standard normal distribution. In other words, about 97.5% of the distribution falls below a z-score of 1.96.
Please take a look here to understand how the Standard Normal Distribution workds:
https://365datascience.com/calculators/tables/snd-table/
The value 0.9750 that you mentioned corresponds to this 97.5%. In a standard normal distribution, the area to the left of z = 1.96 is 0.9750 (or 97.5%). This leaves 2.5% (or 0.0250) in the upper tail. Since a two-tailed test considers both the upper and lower tails of the distribution, the total area in the tails is 5% (0.05), which corresponds to the commonly used alpha level of 0.05 for statistical significance.