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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.