Page 58 - Basic Statistics

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n
 X i
X = i= 1 ( H2 )
n

c. Determine and calculate the test statistic.

2
If the variance of the population ( ) is known or variances of the
2
sample is stable to predict his the population variance ( ), then the test
2
statistic used is the standard normal (z). Variance of sample ( S ) is stable
2
to predict the population variance ( ) when his sample size n  30.
2
Further written S = ˆ  . Statistical test used is the Z-standard normal :
2

X −  X  X 
−
−
z = 0 = 0 or Z = 0 ( H3 )
 x  / n / ˆ  n

If the population variance is unknown and the sample size n < 30, then

the test statistic used is the student-t, as follows

X −  X 
−
t = 0 = 0 ( H4 )
S x / S n

with n-1 degrees of freedom.

d. Establish critical region to reject the null hypothesis. Determination of

the critical region is highly dependent on three things: the formulation of

a alternative hypothesis, test statistics are used and level of significance.

If H :    then critical region
0
1

z > z  2 / or t >t  , 2 / db= n− 1 ( H5 )

~~* CHAPTER 4 HYPOTHESIS TESTING *~~