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Your search for "compare data with predictions and use as evidence in developing explanations" returned 12 result(s)

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ACMSM143

use \(\overline x\) and \(s\) to estimate \(\mu\) and \(\sigma\), to obtain approximate intervals covering desired proportions of values of a normal random variable and compare with an approximate confidence interval for \(\mu\)

ACMSM127

use numerical integration using technology \(f\left(t\right)=\lambda e^{-\lambda t}\) for \(t\geq0\) of the exponential random variable with parameter \(\lambda>0,\), and use the exponential random variables and associated probabilities and quantiles …

ACMSM144

collect data and construct an approximate confidence interval to estimate a mean and to report on survey procedures and data quality.

ACMSM126

use numerical integration using technology

ACMSM119

find and use the inverse trigonometric functions: arcsine, arccosine and arctangent

ACMSM120

find and use the derivative of the inverse trigonometric functions: arcsine, arccosine and arctangent

ACMSM122

use partial fractions where necessary for integration in simple cases

ACMSM118

establish and use the formula \(\int\frac1xdx=\ln{\;\vert x\;\vert}+c\) for x ≠ 0

ACMSM128

use implicit differentiation to determine the gradient of curves whose equations are given in implicit form

ACMSM142

use simulation to illustrate variations in confidence intervals between samples and to show that most but not all confidence intervals contain \(\mu\)

ACMSM117

use substitution \(u = g(x)\) to integrate expressions of the form \(f\left(g\left(x\right)\right)g'\left(x\right)\)

ACMSM136

consider and solve problems involving motion in a straight line with both constant and non-constant acceleration, including simple harmonic motion and the use of expressions \(\frac{dv}{dt}\), \(v\frac{dv}{dx}\) and \(\frac{d(\frac12v^2)}{dx}\) for a …