These questions are designed to help you verify that you can successfully apply the techniques related to maximum-likelihood estimation we have learned in class, e.g., numerical and analytical derivation of estimators, construction of large-sample confidence intervals, and likelihood-ratio tests.

Randomly chooses one of the following

a) Divide numerical fractions. Simplifying is discussed in the advice but not required to get full marks.

b) Divide a negative whole number by a fraction. Simplifying is discussed in the advice but not required to get full marks.

Randomly chooses one of the following

a) Multiply numerical fractions. Simplifying is discussed in the advice but not required to get full marks.

b) Multiply a negative fraction by a whole number. Simplifying is discussed in the advice but not required to get full marks.

Fractions already have a common denominator. Addition and subtraction 50:50 split, when subtracting, the answer is negative half the time. Students shouldn't have to worry about reducing fractions by design.

This question assesses the learner's ability of calculating confidence intervals for numerical data and conducting a one-sample t-test.

Randomized input values: sample summary statistics and confidence level.

Adapted from question 7.12 in OpenIntro Statistics (4th ed).

Fractions don't have a common denominator. Need to find one. Addition and subtraction 50:50 split.

Given cost of production and price of sale of a product; a percentage increase in cost of production; and unit sales before and after; work out the extra profit.

Based on question 6 from section 3 of the maths-aid workbook on numerical reasoning.

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Straightforward solving linear equations question

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Practice with adding, subtracting and dividing basic algebraic fractions

Simplifying indices

Simplifying indices

Simplifying indices

Simplifying indices

Simplifying indices

Simplifying indices

Simplifying indices

Basic solving of linear equations

Basic solving of linear equations

Solving linear equations.

Solving linear equations

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Straightforward solving linear equations question