A long-time authorized user of an account makes 0.2 seconds between keystrokes. One day, data are recorded as someone typed the correct username and password. The average time between keystrokes was 0.3 with a standard deviation equal to 0.1183. The sample size was 25. 1. At a 1% level of significance, is this an evidence of an unauthorized attempt? Hint: Use a statistical test.
2. Can you apply the z-test and the normal approximation of the Z test statistic to this set of data? Are the conditions on the data for the test satisfied?