The response times of two distinct cloud-based microservices, Alpha and Beta, were recorded under peak load conditions. A random sample of 80 requests to Service Alpha resulted in a mean response time of 242 ms with a standard deviation of 32 ms. A separate random sample of 120 requests to Service Beta resulted in a mean response time of 251 ms with a standard deviation of 45 ms.
Test, at the 1% significance level, whether there is evidence that the mean response time of Service Alpha is less than the mean response time of Service Beta. State your hypotheses clearly.
State two assumptions required for the validity of the test in part (a).
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.