A 82% confidence interval for a sampling distribution with a mean of 100, a sample standard deviation of 24 and a sample size of 36 will be based on a á= ______ and a corresponding Zá of ___

To find the value of α, which represents the significance level, we need to subtract the confidence level from 1. Since you mentioned an 82% confidence interval, we subtract 82 from 100 to get 18. Therefore, α = 1 - 0.82 = 0.18.

Now, to find the corresponding Zα value, we need to look up this value in the standard normal distribution table (also known as the Z-table) or use a statistical calculator.

The Zα value signifies the number of standard deviations away from the mean that corresponds to the desired level of confidence. In this case, we want to find the Zα value for a one-tailed test since we are looking for a specific side of the bell curve.

Since α = 0.18, we divide it by 2 (since one tail represents 100 - 82 = 18% of the data) to find the area in one tail, which is 0.09. Next, we look for the value in the Z-table that is closest to 0.09. Interpolating values in the Z-table will give us a more accurate value, but for simplicity, let's assume the closest value is 0.090.

Now, we subtract the area we found (0.090) from 0.5 (which represents the area under the curve on one side). This gives us 0.5 - 0.090 = 0.410.

Looking up this value in the Z-table, we find that Zα ≈ 1.28.

Therefore, the α value for the 82% confidence interval is 0.18, and the corresponding Zα value is approximately 1.28.