Estimate and interpret a confidence interval

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

4 practice marks

Original practice question

In a random sample of 200 voters, 120 support a proposal. Use the approximate interval $\hat p\pm1.96\sqrt{\hat p(1-\hat p)/n}$. (a) Calculate the sample proportion and 95% confidence interval; give endpoints to three decimals. [3 marks] (b) Interpret the 95% confidence level. [1 marks]

Worked explanation

• Part (a)

  $\hat p=120/200=0.6$. The standard error is $\sqrt{0.6(0.4)/200}=0.034641$. Add and subtract $1.96$ standard errors to obtain $[0.532,0.668]$.

• Part (b)

  If the same random sampling and interval procedure were repeated, approximately 95% of the constructed intervals would contain the population proportion. This is a statement about the method, not a 95% probability assigned to the fixed parameter after sampling.

(a) $\hat p=0.6$; $[0.532,0.668]$.; (b) About 95% of intervals from repeated samples cover the fixed population proportion.

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