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 calculate the confidence interval, we need to determine the level of confidence (α) and find the corresponding Zα value from the standard normal distribution table.
Given:
Mean (μ) = 100
Sample standard deviation (σ) = 24
Sample size (n) = 36
The confidence level (α) represents the probability that the true population mean falls within the interval. For an 82% confidence interval, we subtract the confidence level from 1, and divide it by 2 to find the tail probabilities on each side of the distribution:
1 - Confidence level = 1 - 0.82 = 0.18
Tail probability on each side = 0.18 / 2 = 0.09
To find the corresponding Zα value, we look up the cumulative probability of 1 - 0.09 (0.91) in the standard normal distribution table.
The closest Z value for the cumulative probability of 0.91 is approximately 1.34.
Therefore, a 82% confidence interval for the given sampling distribution will be based on a α = 0.18 and a corresponding Zα of approximately 1.34.