5. A dance studio has 800 dancers of which
\begin{displayquote}
452 are beginners
251 are intermediates
97 are professionals
- Explain in detail how a stratified sample of size 50 could be taken.
- State an advantage of stratified sampling rather than simple random sampling in this situation.
\end{displayquote}
Independent random samples of 80 beginners and 60 intermediates are chosen. Each of these dancers is given an assessment score, \(x\), based on the quality of their dancing. The results are summarised in the table below.
| \(\bar { x }\) | \(s ^ { 2 }\) | \(n\) |
| Beginners | 31.7 | 57.3 | 80 |
| Intermediates | 36.9 | 38.1 | 60 |
- Stating your hypotheses clearly and using a \(5 \%\) level of significance, test whether or not these data support the studio manager's belief.