In: Statistics and Probability
Use Excel to obtain a 95% confidence level for the mean satisfaction rating of the new sandwich
Satisfaction |
7 |
5 |
5 |
6 |
8 |
7 |
6 |
7 |
10 |
7 |
9 |
5 |
5 |
8 |
8 |
6 |
7 |
8 |
7 |
5 |
5 |
5 |
5 |
5 |
2 |
5 |
8 |
7 |
6 |
6 |
4 |
6 |
6 |
5 |
6 |
7 |
8 |
9 |
5 |
4 |
Values ( X ) | Σ ( Xi- X̅ )2 | |
7 | 0.5625 | |
5 | 1.5625 | |
5 | 1.5625 | |
6 | 0.0625 | |
8 | 3.0625 | |
7 | 0.5625 | |
6 | 0.0625 | |
7 | 0.5625 | |
10 | 14.0625 | |
7 | 0.5625 | |
9 | 7.5625 | |
5 | 1.5625 | |
5.0 | 1.5625 | |
8 | 3.0625 | |
8 | 3.0625 | |
6 | 0.0625 | |
7 | 0.5625 | |
8 | 3.0625 | |
7 | 0.5625 | |
5 | 1.5625 | |
5 | 1.5625 | |
5 | 1.5625 | |
5 | 1.5625 | |
5 | 1.5625 | |
2 | 18.0625 | |
5 | 1.5625 | |
8 | 3.0625 | |
7 | 0.5625 | |
6 | 0.0625 | |
6 | 0.0625 | |
4 | 5.0625 | |
6 | 0.0625 | |
6 | 0.0625 | |
5 | 1.5625 | |
6 | 0.0625 | |
7 | 0.5625 | |
8 | 3.0625 | |
9 | 7.5625 | |
5 | 1.5625 | |
4 | 5.0625 | |
Total | 250 | 99.5 |
Mean X̅ = Σ Xi / n
X̅ = 250 / 40 = 6.25
Sample Standard deviation SX = √ ( (Xi - X̅
)2 / n - 1 )
SX = √ ( 99.5 / 40 -1 ) = 1.5973
CONFIDENCE.T(0.05,STDEV.S(F3:F42),COUNT(F3:F42)) = 0.5108
CONFIDENCE.T(alpha,standard_dev,size)
alpha = 0.05
standard_dev = STDEV.S(F3:F42) = 1.5973
size = COUNT(F3:F42) = 40
X̅ = AVERAGE(F3:F42) = 6.25
Where, Range(F3:F42) is the range of data values in excel
Confidence interval X̅ ± CI = 6.25 ± 1.5973
95% Confidence interval is ( 5.7391 , 6.7609
)