In testing the difference between two population means using two independent samples, the population standard deviations are assumed to be unknown, each sample size is 30, and the calculated test statistic z = 2.56. If the test is a twotailed and the 5% level of significance has been specified, the conclusion should be:
a. 
none of these answers is correct. 

b. 
choose two other independent samples. 

c. 
reject the null hypothesis. 

d. 
not to reject the null hypothesis. 
z = 2.56
1) Pvalue approach
Pvalue = P( Z > z)......... where Z follows normal(0,1)
= P( Z > 2.56)
= 2 * P(Z > 2.56 )
= 2 * ( 1P( Z < 2.56) )
= 2 * ( 1 0.9948)
= 2* 0.0052
= 0.0105
Pvalue = 0.0105
We reject Ho if Pvalue < alpha = level of significance
Alpha = 0.05
Here Pvalue = 0.0105 < alpha = 0.05
We reject Ho.
2) using a critical value approach
Zc = Zalpha/2 = Z 0.05/2 = Z0.025 = ?
In Normal probability table find value 0.025 & corresponding row value + column value = Zc
Here Zc = 1.96
We reject Ho if Z > Zc
Here Z = 2.56 > Zc = 1.96
We reject Ho.
Answer: c) reject the null hypothesis
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