In math courses at the national campus Spring 2001 the campuswide population mean grade point average (GPA) µ was 1.613. During the Spring 2001 term at the national campus 15 Yapese male students attained a sample mean GPA x of 1.133 with a standard deviation sx of 1.407 in math courses. For a confidence level of 90%, is the Yapese male math GPA statistically significantly different than the national campus math GPA?
Statistic or Parameter | Symbol | Equations | Excel |
---|---|---|---|
Basic Statistics | |||
Square root | Ö | =SQRT(number) | |
Sample size | n | =COUNT(data) | |
Sample mean | x | Sx/n | =AVERAGE(data) |
Sample standard deviation | sx | =STDEV(data) | |
Sample Coefficient of Variation | CV | 100(sx/x) | =100*STDEV(data)/AVERAGE(data) |
Normal Statistics | |||
Calculate a z value from an x | z | ^{= } | =STANDARDIZE(x, m, s) |
Calculate an x value from a z | x | = s z + m | = s*z+m |
Calculate a z value from an x | z | ||
Calculate an x from a z | =m + z_{c}*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 | |
Find a z_{c} value from a confidence level c | z_{c} | =ABS(NORMSINV((1-c)/2)) | |
Find a t_{c} value from a confidence level c | t_{c} | =TINV(1-c,df) | |
Calculate an error tolerance E of a mean for n ³ 30 using sx | E | =z_{c}*sx/SQRT(n) | |
Calculate an error tolerance E of a mean for n < 30 using sx. Can also be used for n ³ 30. | E | =t_{c}*sx/SQRT(n) | |
Calculate a confidence interval for a population mean m from a sample mean x and an error tolerance E | x-E< m <x+E | ||
Hypothesis Testing | |||
Calculate a t-statistic (tstat) | t | ||
Calculate t-critical for a two-tailed test | t_{c} | =TINV(a,df) | |
Calculate t-critical for a one-tailed test | t_{c} | =TINV(2*a,df) | |
Calculate a p-value from a t-statistic | p | = TDIST(ABS(tstat),df,#tails) |