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.
