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).
If a pooled-variance two-sample test were used instead of the test in part (a), state the assumption needed about the population variances.
209 exam-style questions on CCEA A Level Maths 4.6 Statistical hypothesis testing (A-level only), covering 4.6.1 Statistical hypothesis testing (A-level only), 4.6.2 Statistical hypothesis testing (A-level only), 4.6.3 Statistical hypothesis testing (A-level only), 4.6.4 Statistical hypothesis testing (A-level only), and 4.6.5 Statistical hypothesis testing (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.