7.6 Drills: Computational exercises

(Answers appear 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. If you need help, please 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 \(\hat{p} = 0.814\).

Will the CIs be statistically valid in the above situations?