How To Calculate Confidence Interval 6 Steps With Pictures

To calculate the sample mean of the data, just add up all of the weights of the 1,000 men you selected and divide the result by 1000, the number of men. This should have given you the average weight of 180 lbs. [4] X Expert Source Mario Banuelos, PhDAssistant Professor of Mathematics Expert Interview. 11 December 2021. To calculate the sample standard deviation, you will have to find the mean, or the average of the data. Next, you’ll have to find the variance of the data, or the average of the squared differences from the mean. Once you find this number, just take its square root. [5] X Expert Source Mario Banuelos, PhDAssistant Professor of Mathematics Expert Interview. 11 December 2021. Let’s say the standard deviation here is 30 lbs. (Note that this information can sometimes be provided for you during a statistics problem. )

To find the critical value, or Za/2: Here, the confidence level is 95%. Convert the percentage to a decimal, . 95, and divide it by 2 to get . 475. Then, check out the z table to find the corresponding value that goes with . 475. You’ll see that the closest value is 1. 96, at the intersection of row 1. 9 and the column of . 06. To find the standard error, take the standard deviation, 30, and divide it by the square root of the sample size, 1,000. You get 30/31. 6, or . 95 lbs. Multiply 1. 96 by . 95 (your critical value by your standard error) to get 1. 86, your margin of error.

You can also use this handy formula in finding the confidence interval: x̅ ± Za/2 * σ/√(n). Here, x̅ represents the mean.