Provided with information on a sample with sample mean and standard deviation, but no information on the population variance, use the t test to either accept or reject a given null hypothesis.

A set of MCQ designed to help Level 2 Engineering students prepare/practice for the on-line GOLA test that is used to assess the C&G 2850, Level 2 Engineering, Unit 202: Engineering Principles.

Manipulate surds and rationalise the denominator of a fraction when it is a surd.

Is this number divisible by 5? Half the time the number is, half the time it isn't. Steps give the divisibility test and a way to determine the number of fives.

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Straightforward question: student must find the general solution to a second order constant coefficient ODE. Uses custom marking algorithm to check that both roots appear and that the solution is in the correct form (e.g. two arbitrary constants are present). Arbitrary constants can be any non space-separated string of characters. The algorithm also allows for the use of $e^x$ rather than $\exp(x)$.

Unit tests are also included, to check whether the algorithm accurately marks when the solution is correct; when it's correct but deviates from the 'answer'; when one or more roots is incorrect; or when the roots are correct but constants of integration have been forgotten.

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

Paired t-test to see if there is a difference between times taken to complete a task.

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A set of MCQ designed to help Level 2 Engineering students prepare/practice for the on-line GOLA test that is used to assess the C&G 2850, Level 2 Engineering, Unit 202: Engineering Principles.

Given  $P(A)$, $P(A\cup B)$, $P(B^c)$ find $P(A \cap B)$, $P(A^c \cap B^c)$, $P(A^c \cup B^c)$ etc..

Differentiate

\[ \sqrt{a x^m+b})\]

$f(X)$ and $g(X)$ are polynomials over $\mathbb{Z}_n$.

Find their greatest common divisor (GCD) and enter it as a monic polynomial.

Hence factorize $f(X)$ into irreducible factors.

Questions testing understanding of numerators and denominators of numerical fractions.

Given two complex numbers, find by inspection the one that is a root of a given quartic real polynomial and hence find the other roots. 

Double integrals (2) with numerical limits

Multiple response question (2 correct out of 4) covering properties of continuity and differentiability. Selection of questions from a pool.

Can choose true and false for each option. Also in one test run the second choice was incorrectly entered, rest correct,  but the feedback indicates that the third was wrong.

Multiple response question (3 correct out of 6) re properties of convergent and divergent sequences. Selection of questions from a pool.

Double integrals (2) with numerical limits

Multiple response question (2 correct out of 4) covering properties of continuity and differentiability. Selection of questions from a pool.

Can choose true and false for each option. Also in one test run the second choice was incorrectly entered, rest correct,  but the feedback indicates that the third was wrong.

Provided with information on a sample (>30) with sample mean and standard deviation, use the z test to either accept or reject a given null hypothesis.

Two sample t-test to see if there is a difference between scores on questions between two groups when the questions are asked in a different order.

For a sample of size n from a normal distribution, given mean of the sample mean and the standard deviation , find the t-statistic corresponding to a null hypothesis $\mu=m$ and a given confidence level. Check if the result is significant at this level.

Straightforward question: student must find the general solution to a second order constant coefficient ODE. Uses custom marking algorithm to check that both roots appear and that the solution is in the correct form (e.g. two arbitrary constants are present). Arbitrary constants can be any non space-separated string of characters. The algorithm also allows for the use of $e^x$ rather than $\exp(x)$.

Unit tests are also included, to check whether the algorithm accurately marks when the solution is correct; when it's correct but deviates from the 'answer'; when one or more roots is incorrect; or when the roots are correct but constants of integration have been forgotten.

Two sample t-test to see if there is a difference between scores on questions between two groups when the questions are asked in a different order.

Provided with information on a sample with sample mean and known population variance, use the z test to either accept or reject a given null hypothesis.

Three questions on parametric hypothesis testing and confidence intervals, aimed at psychology students.

Provided with information on a sample with sample mean and standard deviation, but no information on the population variance, use the t test to either accept or reject a given null hypothesis.

Provided with information on a sample with sample mean and standard deviation, but no information on the population variance, use the t test to either accept or reject a given null hypothesis.

No description given