Question

In: Statistics and Probability

Use Excel to obtain a 95% confidence level for the mean satisfaction rating of the new...

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

Solutions

Expert Solution

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 )


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