OCR S3 2011 June — Question 2

Exam BoardOCR
ModuleS3 (Statistics 3)
Year2011
SessionJune
TopicCentral limit theorem
TypeProportion confidence interval

2 The population proportion of all men with red-green colour blindness is denoted by \(p\). Each of a random sample of 80 men was tested and it was found that 6 had red-green colour blindness.
  1. Calculate an approximate \(95 \%\) confidence interval for \(p\).
  2. For a different random sample of men, the proportion with red-green colour blindness is denoted by \(p _ { s }\). Estimate the sample size required in order that \(\left| p _ { s } - p \right| \leqslant 0.05\) with probability \(95 \%\).
  3. Give one reason why the calculated sample size is an estimate.