Test of Hypothesis: Z-Test Of Difference Between Two Means (Essay Sample)

Z-TEST OF DIFFERENCE BETWEEN TWO MEANS
Institution:
Name:
Assuming that u1 and u2,represents means of two population of interest,
The hull hypothesis for comparing the two means is :
H0 : μ1 =μ2
The alternative hypothesis can be any of the following below:
HI : μ1 ≠u2
H1: u1< u2
H1 : u1>u2
Depending with the desire of the researcher, a suitable Type I error probability (α) is chosen for the test, the data collection is carried out and the test is carried out using the formula below:
Z= ϑ1-ϑ2δ1n1+δ2n2
Where δ1, δ2 are standard deviations of the two popuplations
n1, n2 are sample sizes and ϑ1,ϑ2 are sample means of the saples obtained from the populations
The Null Hypothesis is rejected in favor of Alternative Hypothesis if:
For HI : μ1 ≠u2 then, Z>Zα2or Z
For H1 : u1>u2 then, Z>Z1-α
For H1: u1< u2 then, Z
It is very important to note that comparing the p- value to α is the same as comparing z- statistic to the cut- off z-value shown above.
This test is commonly used when the sample sizes are large or if the population variances are known.
If the population variance is unknown and it is possible it can be estimated from sample itself, then t-test becomes the most appropriate.
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