approximate confidence interval

Practise approximate confidence interval with an original VectorPaths question, worked explanation and related VCE Methods practice.

3 practice marks

Original practice question

A random sample of 100 people contains 60 who choose option A. Using $\hat p\pm1.96\sqrt{\hat p(1-\hat p)/n}$, find an approximate 95% confidence interval for the population proportion. Give endpoints to three decimal places.

Worked explanation

• Calculate the sample proportion

  $\hat p=60/100=\frac{3}{5}$.

• Calculate standard error and margin

  $SE=\frac{\sqrt{6}}{50}$ and margin $=1.96\times SE=0.096020$.

• Form and interpret the interval

  The approximate interval is $[0.504,0.696]$. In repeated random sampling, about 95% of intervals constructed by this method cover the fixed population proportion.

Approximate interval $[0.504,0.696]$.

Original VectorPaths practice; not an official VCAA question or marking rubric.