Name: _______________________________
In math courses at the national campus Spring 2001 the campuswide population mean grade point average (GPA) m was 1.613. During the Spring 2001 term at the national campus 15 Yapese male students attained a sample mean GPA of 1.133 with a standard deviation sx of 1.407 in math courses. At an alpha a of 0.1, is the Yapese male math GPA statistically significantly lower than the national campus math GPA?
Statistic  Equations  Excel 

Square root  =SQRT(number)  
Sample size  n  =COUNT(data) 
Sample mean  =AVERAGE(data)  
Population mean  m x P(x) n p (binomial) 
=AVERAGE(data) 
Sample standard deviation  sx 
=STDEV(data) 
Population standard deviation  s (binomial) 
=STDEVP(data) 
Slope  =SLOPE(y data, x data)  
Intercept  =INTERCEPT(y data, x data)  
Correlation  =CORREL(y data, x data)  
Binomial probability  =_{ n}C_{r} p^{r} q^{(nr)}  =COMBIN(n,r)*p^r*q^(nr) 
Calculate a z value from an x  ^{z = }  =STANDARDIZE(x, m, s) 
Calculate an x value from a z  x = s z + m  
Calculate a z value from an value given m and s  =STANDARDIZE(x, m, s/SQRT(n))  
Find a probability p from a z value  =NORMSDIST(z)  
Find a z value from a probability p  =NORMSINV(p)  
Standard error of the population mean  
Standard error of the sample mean  
Determining z critical z_{c} from a for confidence intervals or twotail tests.  =NORMSINV(1a/2)  
Error tolerance E of a mean for n ³ 30 using s  =CONFIDENCE(a,s,n)  
Error tolerance E of a mean for n ³ 30 using sx  E =  =CONFIDENCE(a,sx,n) 
Error tolerance E of a mean for n < 30. Can also be used for n ³ 30.  [no Excel function, determine t_{c} and then multiply by standard error of the mean as shown in the equation]  
Determining t_{c} from a and the degrees of freedom df for a confidence interval or a twotail test.  =TINV(a,df)  
Calculate an value from a t_{c}  =+ m  
Calculate a confidence interval for a population mean m from a sample mean and an error tolerance E  E< m <+E  
Determining z_{c} from a for a twotail hypothesis test.  =NORMSINV(a/2) [returns only the negative value for z_{c}] 

Determining z_{c} from a for a onetail hypothesis test.  =NORMSINV(a) [returns the right tail z_{c}, change the sign for the left tail] 

Determining t_{c} from a and degrees of freedom df for a twotail hypothesis test.  =TINV(a, df) [returns only the positive value for t_{c}] 

Determining t_{c} from a and degrees of freedom df for a onetail hypothesis test.  =TINV(2a, df) [returns only the lefttail t_{c}, change the sign for righttail] 

Determining the onetail pvalue for a zstatistic z for a negative value of z  =NORMSDIST(z)  
Determining the onetail pvalue for a zstatistic z for a positive value of z  =NORMSDIST(1z)  
Determining the twotail pvalue for the absolute value of the zstatistic  =2*NORMSDIST(1z)  
Determining the onetail pvalue for a tstatistic t and degrees of freedom df  =TDIST(t,df,1) [TDIST accepts only positive values for t, use the absolute value of t] 

Determining the twotail pvalue for a tstatistic t and degrees of freedom df  =TDIST(t,df,2) 