0.95 degree of confidence find the confidence interval for the mean of the whole population
To find the confidence interval for the mean of the whole population at a specific level of confidence, you need to use the formula:
Confidence Interval = (Sample Mean) ± (Critical Value) x (Standard Error)
1. Determine the sample mean: This is the mean of the sample you have collected from the population.
2. Determine the critical value: The critical value depends on the desired confidence level and the sample size. You need to consult a standard statistical table or use a statistical calculator to find the critical value. For example, if you want a 95% confidence level, the critical value for a large sample (typically, if the sample size is greater than 30) is typically 1.96.
3. Calculate the standard error: The standard error measures the variability of the sample mean. The formula for the standard error is:
Standard Error = (Sample Standard Deviation) / √(Sample Size)
If you have the population standard deviation, you can use that instead of the sample standard deviation. If the sample size is large (typically if it is greater than 30), you can use the sample standard deviation as an estimate of the population standard deviation.
4. Plug in the values: After obtaining the sample mean, critical value, and standard error, you can use the formula to calculate the confidence interval. Add the critical value multiplied by the standard error to the sample mean, and subtract it as well to create the interval around the sample mean.
For example, if the sample mean is 50, the critical value is 1.96, and the standard error is 2.5, the confidence interval would be:
Confidence Interval = 50 ± 1.96(2.5)
This would result in a confidence interval between 44.65 and 55.35.
Remember, the confidence interval represents the range of values within which we can be confident that the population mean falls, given the sample data and desired level of confidence.