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.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.