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 A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.