WACE Maths Methods ATAR Paper 1 Topic Tests
Confidence Intervals for Proportions Topic Test 1
Section One: Technology-free
Number of marks: 5
Reading time: 1 minute
Writing time: 5 minutes
Section One:
Answer all questions. Write your answers in the spaces provided.
Supplementary pages for planning/continuing your answers to questions are provided at the end of this Question/Answer booklet. If you use these pages to continue an answer, indicate at the original answer where the answer is continued, i.e. give the page number.
Two independent samples of different sizes were taken from a population. The first sample had sample size \(n_1\) and the second sample had sample size \(n_2\). The sample proportions of males in the samples were the same. When 99% confidence intervals were calculated for each sample, it was found that the corresponding margin of error in the second sample was half that of the first sample.
What is the ratio of the two sample sizes, \(\frac{n_2}{n_1}\)?
A 95% confidence interval for a population proportion based on a sample size of 200 has width \(w\). What sample size is required to obtain a 95% confidence interval of width \(\frac{w}{3}\)?
End of questions
