A systems engineer is evaluating the signal latency of two satellite transmission protocols, Protocol P\mathcal{P}P and Protocol Q\mathcal{Q}Q. They suspect that Protocol P\mathcal{P}P results in a significantly lower mean latency than Protocol Q\mathcal{Q}Q. A random sample of 80 transmissions using Protocol P\mathcal{P}P yielded a mean latency of 124.5 ms with a standard deviation of 12.4 ms. A second random sample of 100 transmissions using Protocol Q\mathcal{Q}Q yielded a mean latency of 128.2 ms with a standard deviation of 15.6 ms.
Stating your hypotheses clearly and using a 1% level of significance, determine whether there is sufficient evidence to support the engineer's suspicion.
162 exam-style questions on AQA A Level Maths 2.5 O: Statistical hypothesis testing, covering 2.5.1 Language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, and 2.5.3 Hypothesis test for a Normal mean (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.