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 two-tailed 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) P-value approach
P-value = P( |Z| > z)......... where Z follows normal(0,1)
= P( |Z| > 2.56)
= 2 * P(Z > 2.56 )
= 2 * ( 1-P( Z < 2.56) )
= 2 * ( 1- 0.9948)
= 2* 0.0052
= 0.0105
P-value = 0.0105
We reject Ho if P-value < alpha = level of significance
Alpha = 0.05
Here P-value = 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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