How would I find the confidence level (in %) if I am given the standard deviation, size of the random sample, and confidence interval?
To find the confidence level in percentage, you need to know the formula for a confidence interval. The formula for a confidence interval is:
Confidence Interval = mean ± (Z * (standard deviation / √n))
In this formula, "mean" represents the sample mean, "Z" is the Z-score (the number of standard deviations from the mean), "standard deviation" is the standard deviation of the population, and "n" is the size of the random sample.
To find the confidence level, you need to calculate the critical value for the Z-score using a Z-table or a statistical calculator. The critical value represents the number of standard deviations needed to achieve a specific confidence level. Once you have the critical value, you can use it to determine the confidence level.
Here are the steps to find the confidence level:
1. Determine the critical value (Z-score) based on the desired confidence level. For example, if you want a 95% confidence level, the critical value would be 1.96 (for a two-tailed test).
2. Plug in the given values into the formula for the confidence interval and solve for the margin of error. The margin of error is calculated as Z * (standard deviation / √n).
3. Once you have the margin of error, subtract it from the sample mean and add it to the sample mean to get the lower and upper bounds of the confidence interval, respectively.
4. To find the confidence level, calculate the probability that a random interval of the same size from the population will include the population mean. This is typically expressed as a percentage.
For example, let's say you have a random sample of size 100, a standard deviation of 10, and a confidence interval of 4. Using the formula, you find the margin of error by multiplying the critical value (Z-score) by the standard deviation divided by the square root of the sample size. Once you have the margin of error, you subtract it from the sample mean and add it to the sample mean to get the lower and upper bounds of the confidence interval, respectively. Finally, you can calculate the confidence level by comparing the confidence interval to the population mean.
Please note that the confidence level is not directly provided by these given parameters, but rather it is calculated using the formula and critical values.