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.
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.