### MS 150 Statistic Quiz 7 Spring 2002 8.1

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.

1. ________ What is z-critical?
2. ________ What is the error E?
3. The confidence interval for the population mean µ is: _______ < µ < _______
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