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 - zscoreα/2 * s/√n < μ < X + zscoreα/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 zscore0.05 = 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 + zscoreα * 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 - zscoreα * 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
You have 2 free calculationss remaining
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?