In the soy sauce survey the volumes of 37 bottles of soy sauce were recorded. The mean volume is 889 milliliters with a sample standard deviation of 590 milliliters. Construct a 95% confidence interval for the population mean volume for soy sauce based on this data.
Statistic or Parameter | Symbol | Equations | Excel |
---|---|---|---|
Normal Statistics | |||
Calculate a z value from an x | z | = | =STANDARDIZE(x, µ, s) |
Calculate an x value from a z | x | = s z + µ | =s*z+µ |
Calculate a z-statistic from an x | z | =(x - µ)/(sx/SQRT(n)) | |
Calculate a t-statistic (t-stat) | t | =(x - µ)/(sx/SQRT(n)) | |
Calculate an x from a z | =µ + zc*sx/sqrt(n) | ||
Find a probability p from a z value | =NORMSDIST(z) | ||
Find a z value from a probability p | =NORMSINV(p) | ||
Confidence interval statistics | |||
Degrees of freedom | df | = n-1 | =COUNT(data)-1 |
Find a zc value from a confidence level c | zc | =ABS(NORMSINV((1-c)/2)) | |
Find a tc value from a confidence level c | tc | =TINV(1-c,df) | |
Calculate an error tolerance E of a mean for n >= 30 using sx | E | =zc*sx/SQRT(n) | |
Calculate an error tolerance E of a mean for n < 30 using sx. Can also be used for n >= 30. | E | =tc*sx/SQRT(n) | |
Calculate a confidence interval for a population mean µ from a sample mean x and an error tolerance E | x-E<= µ <=x+E |
Store | Brand | Price | Volume/ml |
Ace Comm | Yamasa | 0.55 | 150 |
Ace Comm | Yamasa | 1.6 | 500 |
Ace Comm | Yamasa | 3.95 | 1000 |
Ace Comm | Yamasa | 5.95 | 1800 |
Ambros | Kikkoman | 1.65 | 600 |
Ambros | Kikkoman | 3.85 | 1000 |
Bamboo Inn | Yamasa | 1.85 | 500 |
Best Buy | Kikkoman | 1.10 | 148 |
Best Buy | Kikkoman | 2.03 | 296 |
Best Buy | Kikkoman | 3.13 | 591 |
Best Buy | Kikkoman | 5.54 | 1890 |
En's 7 Star | Kikkoman | 1.25 | 148 |
En's 7 Star | Yamasa | 2.1 | 500 |
En's 7 Star | Yamasa | 4.95 | 1000 |
En's 7 Star | Yamasa | 6.25 | 1800 |
Josaiah | Kikkoman | 3.9 | 1000 |
Josaiah | Yamasa | 1.9 | 500 |
Nakasone | Kikkoman | 2.25 | 500 |
Nakasone | Kikkoman | 3.97 | 1000 |
Nakasone | Kikkoman | 3.97 | 1000 |
Nakasone | Kikkoman | 4.69 | 1800 |
Palm Terrace | Kikkoman | 1.15 | 148 |
Palm Terrace | Kikkoman | 1.29 | 296 |
Palm Terrace | Kikkoman | 2.48 | 591 |
Palm Terrace | Kikkoman | 4.28 | 1200 |
Palm Terrace | Kikkoman | 6.28 | 1890 |
Panuelo | Kikkoman | 1.45 | 148 |
Panuelo | Kikkoman | 2.96 | 296 |
Panuelo | Yamasa | 1.95 | 500 |
Panuelo | Yamasa | 4.75 | 1000 |
Panuelo | Yamasa | 5.15 | 1800 |
Wall Mart | Kikkoman | 1.85 | 600 |
Wall Mart | Kikkoman | 5.40 | 1600 |
Wall Mart | Yamasa | 5.4 | 1800 |
Yoshie | Kikkoman | 1.90 | 500 |
Yoshie | Kikkoman | 3.40 | 1000 |
Yoshie | Kikkoman | 5.50 | 1800 |