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.
130 exam-style questions on WJEC A Level Maths 4.3.2 Statistical hypothesis testing (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.