A financial technologist monitored the latency, measured in milliseconds (ms), of a high-frequency trading algorithm. Over a period of one week, a random sample of 150 execution cycles showed a mean latency of 12.4 ms12.4 \text{ ms}12.4 ms with a standard deviation of 3.2 ms3.2 \text{ ms}3.2 ms. After upgrading the network hardware, a second random sample of 180 execution cycles was taken, which showed a mean latency of 11.6 ms11.6 \text{ ms}11.6 ms with a standard deviation of 2.1 ms2.1 \text{ ms}2.1 ms.
Test at the 5%5\%5% level of significance whether the mean latency of the trading algorithm decreased after the hardware upgrade. State your hypotheses clearly.
Explain the significance of the Central Limit Theorem to the test conducted in part (a).
State an assumption you have made regarding the sample variances to perform this test.
132 exam-style questions on Edexcel A Level Maths 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.