ACMMM178
use the approximate confidence interval \(\left(\widehat p-z\sqrt[{}]{(\widehat p(1-\widehat p)/n},\;\;\widehat p+z\sqrt[{}]{(\widehat p(1-\widehat p)/n}\right),\) as an interval estimate for \(p\), where \(z\) is the appropriate quantile for the standard …
ACMMM178 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM156
recognise the qualitative features of the graph of \(y=\log_ax\) \((a>1)\) including asymptotes, and of its translations \(y=\log_ax+b\) and \(y=\log_a{(x+c)}\)
ACMMM156 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM179
define the approximate margin of error \(E=z\sqrt[{}]{(\widehat p(1-\widehat p)/n}\) and understand the trade-off between margin of error and level of confidence
ACMMM179 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM176
simulate repeated random sampling, for a variety of values of \(p\) and a range of sample sizes, to illustrate the distribution of \(\widehat p\) and the approximate standard normality of \(\frac{\widehat p\;-p}{\sqrt[{}]{(\widehat p(1-\widehat p)/n}}\) …
ACMMM176 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum