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 ____
.18 and .47
.18 and .915.
.09 and .23
.09 and 1.34
I'll give you a hint: + or - 1.34 represents the 82% confidence interval using a z-table.
truye
To determine the Á level and corresponding Zá value for a given confidence interval, we can use the formula:
Zá = (X - µ) / (σ / √n)
Where:
Á is the confidence level, also known as the level of significance.
X is the sample mean.
µ is the population mean.
σ is the population standard deviation.
n is the sample size.
In this case, we are provided with the following information:
Sample mean (X) = 100
Sample standard deviation (σ) = 24
Sample size (n) = 36
We need to find the Á level and corresponding Zá value for an 82% confidence interval.
Step 1: Convert the confidence level to a decimal.
82% = 0.82
Step 2: Determine the Á level.
The Á level is equal to 1 minus the confidence level.
Á = 1 - 0.82 = 0.18
Step 3: Find the corresponding Zá value.
To find the Zá value, we can refer to the standard normal distribution table.
Looking up the value of 0.18 in the table, we find that the closest value is 0.915.
Therefore, the correct answer is:
A 82% confidence interval for the given sampling distribution will be based on a Á level of 0.18 and a corresponding Zá value of 0.915.