Two-Sample Z-Test
The Two-Sample Z-test is used to compare the means of two samples to see if it is feasible that they come from the same population. The null hypothesis is: the population means are equal. The Z-test is preferred to the t-test for large samples (N > 30) or when the variance is known, otherwise, the sample standard deviation is a more biased estimate of a population standard deviance than is allowable, and using a two-sample t-test should be considered (see the Comparing Means command).
Assumptions
1. Normal but independent populations.
2. Variances for populations are known.
How To
Run: Statistics→Basic Statistics→Two-Sample Z-Test for Means...
Select two variables.
Enter variances for both populations (known).
Enter the hypothesized means difference. A value of 0 (zero) indicates that the means are hypothesized to be equal.
Results
Mean, Variance, Sample Size – the mean, variance and size of an input variable. See the Descriptive Statistics procedure for more information.
Mean Difference – difference between the means.
Standard Error - estimated standard error for the difference between means.
z (Test statistic) – z-score, the distance between means in units of the standard error.
Z – critical value for z.
P(Z<=z) p-level – probability of observing the sample statistic as extreme as the test statistic. If the null hypothesis is and the two-tailed p-value is less than (0.05), the conclusion is that, statistically, the means are significantly different.
References
Sprinthall, R. C. (2011). Basic Statistical Analysis (9th ed.). Pearson Education.