## 6.8 **Drills**: Computational exercises

*(Answers are available in Sect. A.6)*

These **Drill** exercises (repeated practice) give you practice at getting computations correct,
and using your calculator.
These drill questions are more about practising the underlying *mathematics* rather than the *statistics*.

**ask**.

The *standard error* for a sample proportion is calculated as

\[ \text{s.e.}(\hat{p}) = \sqrt{\frac{\hat{p} \times (1 - \hat{p})}{n}}. \] The standard error quantifies how much the sample proportion is likely to vary from sample to sample.

Compute the standard error in these situations:

- When \(n = 25\) and \(\hat{p} = 0.70\).
- When \(n = 100\) and \(\hat{p} = 0.25\).
- When \(n = 32\) and \(\hat{p} = 0.42\).
- When \(n = 53\) and \(\hat{p} = 0.814\).