Since you were not sure what test to use, we evaluate our sample size of n = 1007 Since our sample size was greater than 30, we use the Large Sample Normal Distribution Confidence Interval Test

A large sample of 1007 units has a mean 11.3 and a standard deviation σ of 16.6. Find a 90% confidence interval of the mean μ

Confidence Interval Formula for μ is as follows: X - zscore_{α/2} * s/√n < μ < X + zscore_{α/2} * s/√n where: X = sample mean, s = sample standard deviation, zscore = Normal distribution Z-score from a probability where α = (1 - Confidence Percentage)/2

Find z-score for α value for 0.05 zscore_{0.05} = 1.645 <--- Value can be found on Excel using =NORMSINV(0.95)

Calculate the Standard Error of the Mean:

SEM =

σ

√n

SEM =

16.6

√1007

SEM =

16.6

31.733263305245

SEM = 0.5231

Calculate high end confidence interval total: High End = X + zscore_{α} * s/√n High End = 11.3 + 1.645 * 16.6/√1007 High End = 11.3 + 1.645 * 0.5231103980805 High End = 11.3 + 0.86051660484242 0.86051660484242 can be derived on Excel below

Excel or Google Sheets formula:

Excel or Google Sheets formula:CONFIDENCE(0.1,16.6,1007)

High End = 12.1605

Calculate low end confidence interval total: Low End = X - zscore_{α} * s/√n Low End = 11.3 - 1.645 * 16.6/√1007 Low End = 11.3 - 1.645 * 0.5231103980805 Low End = 11.3 - 0.86051660484242 Low End = 10.4395

Now we have everything, display our 90% confidence interval:

10.4395 < μ < 12.1605

What this means is if we repeated experiments, the proportion of such intervals that contain μ would be 90%

What is the Answer?

10.4395 < μ < 12.1605

How does the Confidence Interval for the Mean Calculator work?

Free Confidence Interval for the Mean Calculator - Calculates a (90% - 99%) estimation of confidence interval for the mean given a small sample size using the student-t method with (n - 1) degrees of freedom or a large sample size using the normal distribution Z-score (z value) method including Standard Error of the Mean. confidence interval of the mean This calculator has 5 inputs.

What 1 formula is used for the Confidence Interval for the Mean Calculator?