juljana wrote:The students are not from the same school. I intend to randomly select students from different schools , from all three areas. Since it is a doctoral research, and not an agency scientific research, it would be more convenient for me to be around 1000 students and some more, but how to divide between cities and age.

Your plan's data-matrix has 15 cells. Unless there is a reason to do otherwise, why not take the same sample size in each cell? If you analyze a total of n=1,000 questionnaires, you would have 66 per cell. For n=1,500 you would have 100 per cell.

For n=1,500 total, that would give you 500 per city and 300 per age group.

If you can come up with an estimate of the standard deviation of Likert Scale data at about the same overall mean score that you expect, it would be possible to estimate the size of difference that would be significant between cities and between age groups. This would help to get a further feel for the effect of sample size. It only needs to be a rough estimate of SD for this purpose, because you will be able to use the actual data in the analysis after you collect it. Perhaps you have some prior data on that.

For total n=1,000:

To compare cities, n=500 vs 500.

To compare age groups, n=300 vs 300.

To compare two age groups within a city, n=100 vs 100.

The smaller total (n=1,000) would work too, but would just be less sensitive.

Also, what kind of analysis of results are you planning?