Homework Soursethe variance of the two populations must be same otherwise v
the variance of the two populations must be same otherwise value of the test static cannot be determined.
show/explain why this is a reasonable assumption.
Solution
The Null Hypothesis should be an assumption about the difference in the population means for two populations (note that the same quantitative variable must have been measured in each population). The data should consist of two samples of quantitative data (one from each population). The samples must be obtained independently from each other.
The samples must be drawn from populations which have known Standard Deviations (or Variances). Also, the measured variable in each population (generically denoted x1 and x2) should have a Normal Distribution.
Note that if the distributions of the variables in the populations are non-normal (or unknown), the two-sample z-test can still be used for approximate results, provided the combined sample size (sum of sample sizes) is sufficiently large. Historically, a combined sample size of at least 30 has been considered sufficiently large; reality is much more complicated.
