A software engineering team monitors bug reports for their new operating system. Historically, 15% of users report encountering an "interface lag" during their first week of use. After a minor kernel update, a random sample of 20 users is monitored, and it is found that 6 of them encountered the lag.
Stating your hypotheses clearly, and using a 5% level of significance, test whether or not there has been a change in the proportion of users encountering interface lag.
A new graphics driver was also bundled with the update. Previously, the proportion of users reporting "system crashes" was 20%. The lead developer claims that the proportion of users encountering crashes has now increased. A random sample of 150 users is surveyed, and it is found that 42 of them reported a system crash.
Using a suitable approximation and stating your hypotheses clearly, test the developer's claim at the 1% level of significance.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.