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.
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.