data from sample of 400 cases, variable has 95% confidence interval of 54.3 to 54.7
I found the mean-
how do i find standard error- step by step please.
Standard error = sd/√n
Note: sd = standard deviation; n = sample size.
You'll need to determine the standard deviation in order to find the standard error.
I'm assuming you determined the mean to be 54.5; therefore, you can determine standard deviation using the following method.
.2 = 1.96 (sd/√400) -->.2 represents the margin of error.
Solve for standard deviation, then you will be able to determine the standard error.
I hope this will help.
To find the standard error, you can use the following steps:
Step 1: Calculate the margin of error.
The margin of error is given as 0.2, which represents a 95% confidence interval. For a 95% confidence interval, the margin of error can be determined by multiplying the standard deviation with the appropriate z-score. In this case, the z-score is 1.96 (corresponding to a 95% confidence level).
Margin of error = 1.96 * standard deviation
Step 2: Rearrange the formula to solve for the standard deviation.
Dividing both sides of the equation by 1.96 gives:
Standard deviation = Margin of error / 1.96
Step 3: Substitute the known values and solve.
Using the given margin of error of 0.2, calculate the standard deviation:
Standard deviation = 0.2 / 1.96
Step 4: Calculate the standard error.
Finally, divide the standard deviation by the square root of the sample size (n) to find the standard error:
Standard error = Standard deviation / √n
Given that n = 400, substitute the values into the equation:
Standard error = (0.2 / 1.96) / √400
Simplifying further:
Standard error = 0.2 / (1.96 * √400)
By evaluating the expression, you will be able to find the standard error.