### MS 150 Statistic Quiz 8 Spring 2002 8 - 9

Sixteen healthy and properly nourished babies 30 months old were found to have a mean mass of 13.2 kilograms with a standard deviation of 8.1 kilograms. A study done on the Pacific Island atoll of Minto found the babies there had a mean mass of 9.0 kilograms. Using a confidence level of 0.95 and the t-distribution, is the Minto mean baby mass statistically significantly different from the population mean for the population of health and properly nourished babies?

1. ________ What is t-critical?
2. ________ What is the error E?
3. The confidence interval for the population mean µ is: _______ < µ < _______
4. ________ Is the Minto mean baby mass statistically significantly different from the population mean for the population of health and properly nourished babies?
5. ________ Are the Minto atoll babies underweight?
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