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 400 people contains 264 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

  $\hat p=264/400=\frac{33}{50}$.

• Calculate standard error and margin

  $SE=\frac{\sqrt{561}}{1000}$ and margin $=1.96\times SE=0.046423$.

• Form and interpret the interval

  The approximate interval is $[0.614,0.706]$. In repeated random sampling, about 95% of intervals constructed by this method cover the fixed population proportion.

Approximate interval $[0.614,0.706]$.

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