A random sample of 400 items is found to have mean of 82 and S.D of 18.find 95% confidence Limits for the mean of the population from which the sample is drawn
The formula for confidence interval for the mean is:
Confidence interval = mean ± Z * (standard deviation / √n)
Where:
mean = 82
standard deviation = 18
n = 400
Z = Z-score for 95% confidence level, which is 1.96
Plugging in the values:
Confidence interval = 82 ± 1.96 * (18 / √400)
Confidence interval = 82 ± 1.96 * (18 / 20)
Confidence interval = 82 ± 1.96 * 0.9
Confidence interval = 82 ± 1.764
Therefore, the 95% confidence interval for the mean of the population from which the sample is drawn is 80.236 to 83.764.