For testing the statistical significance of the difference in heights of school children -
Student's t test
chi-square test
Paired 't' test
ANOVA
Student’s t-test:

– Paired Student’s t-test: Comparing means (± SD) in paired data (in same group of individuals before and after an intervention)

Comparison of mean levels can be done by Paired Student’s t - test

– Unpaired Student’s t-test: Comparing means (± SD) in two different group of individuals

ANOVA test (F-test/F-ratio): Comparing means (+ SD) in more than two different group of individuals
Chi-square test (c2-test): Comparing percentage, proportions & fractions in two or more different group of individuals

In the given question, we have to test the statistical significance of the difference in heights of school children; thus mean heights of schools children in different classes/standards/schools will be done Thus, ANOVA test (F - test/ F -ratio) is most suitable.