H2 Math Summary Notes

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Pure Mathematics
Unit 1 Inequalities
Basics of Test Point Method
Unit 2 Graphing Techniques
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Unit 3 Transformation of Graphs
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Unit 4 Functions
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How to Use GC to Plot an Inverse Graph
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Unit 5 APGP & Recurrence Relations
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Unit 6 Sigma Notation
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Unit 7 Techniques of Differentiation
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Unit 8 Applications of Differentiation
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Unit 9 Maclaurin Series
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Unit 10 Techniques of Integration
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Unit 11 Applications of Integration
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Unit 12 Differential Equations
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Unit 13 Vectors
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Unit 14 Complex Numbers
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Statistics
Unit 15 Permutation and Combinations
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Unit 16 Probability
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Unit 17 Discrete Random Variable
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Unit 18 Binomial Distribution
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Unit 19 Normal Distribution
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Unit 20 Sampling and Estimation
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Unit 21 Hypothesis Testing
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Unit 22 Correlation and Linear Regression
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Worked Example 3

H2 Math Summary Notes Unit 21 Hypothesis Testing Worked Example 3

A beverage company produces thousands of cans of soda each day. The volume of a soda in a can follows a normal distribution with mean [latex]355[/latex] ml and standard deviation [latex]1.2[/latex] ml.

Following the maintenance of the filling machine, there may have been a slight adjustment. To determine if the machine still produces [latex]355[/latex] ml of soda per can, [latex]15[/latex] randomly chosen cans are chosen. The volume, [latex]x[/latex] ml, of the [latex]15[/latex] cans of soda is summarised by

[latex]\sum{x}=5314.5[/latex], [latex]\sum{{{x}^{2}}=1892040.25}[/latex]

Assuming that the variance of the distribution is unaltered by the adjustment, test at the [latex]6\%[/latex] significance level whether there is any change in the mean volume of the soda.

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