Page 229 - Six Sigma Demystified

Part 3 s i x s i g m a to o l s 209

Two-Sided Example at 95% Confidence

Upper (results in calculated value of 26.406) = 25.7 + CONFIDENCE(0.05, 1.8, 25)

Lower (results in calculated value of 24.994) = 25.7 – CONFIDENCE(0.05, 1.8, 25)

One-Sided Example at 95% Confidence

Lower (results in calculated value of 25.108) = 25.7 – CONFIDENCE(0.10, 1.8, 25)

Historical Standard Deviation Is Not Known
Calculate an average ( X ) and the sample standard deviation s of n sample
units.
Calculate the confidence interval as

X − t α / , n −1 s ( / n < µ < X + t α / , n −1 s ( / n)
)
2
2
Based on the assumption that the samples are from a population with a
normal distribution, we use the Student’s t distribution to determine the t val-
ues based on a confidence level. For a 95% confidence level, α = 0.05, so α/2 =
0.025.
For example, the average waiting time in a doctor’s office using a sample of

25 patients is 25.7 minutes. The sample standard deviation is calculated as 1.8
minutes. From Appendix 2, t 0.025,24 = 2.064. The confidence interval is calcu-
lated as

X − t α / , n −1 s ( / n < µ < X + t α / , n −1 s ( / n)
)
2
2
8
1
)
( .8
25 .7 − . 2 064 1 / 25 < µ < 25 .7 + . 2 064 ( . / 25 )
/
24 .96 < µ < 26 .44
Both Excel and Minitab offer confidence interval calculations. Minitab
requires the raw data. In Excel, you can use its other functions to calculate the
required input parameters when using raw data.