part ii) of this question asks to test a hypothesis that Italian managers are dismissed more quickly than English managers. when I am testing this, do i need to use a t-statistics (because n=20 here, and df = 20-1=19), or a z-statistics? the solution does not tell. am a bit confused because the course notes say the estimates approach a normal distribution. i have decided to use a t-test here because of the sample size, is it correct? i mean the conclusion is the same under both of them but i want to know how which test to choose if a similar question comes up in the exam.
Since the estimator arises as a result of maximum likelihood estimation, we know that its asymptotic distribution is normal. So, we'd use a normal distribution in a test (z-statistic) as an approximation (even though the sample size is not approaching infinity). We'd also use a normal confidence interval, if asked for a confidence interval. I don't think I've seen a t distribution used anywhere in the CT4 exam or examiners reports.
hi. can you please exlplain how can we say that "it is not statistically significant" looking at the variance without carrying out a test?
For t between 11 and 12: F(t) for the Italian managers is 0.268. F(t) for the England managers is 0.233. The variance of those values is 0.0106 (Italy) and 0.0104 (England), giving an approx standard deviation of 0.10. The difference between the F(t) values (0.268 - 0.233 = 0.035) is much less than one standard deviation, which wouldn't be statistically significant if we did a test.
Hi, I also have one doubt in this question Why were those managers not considered who joined in between season after someone got sacked or left voluntarily, because usually managers are replaced immediately. OR Do we have to assume that the clubs which sacked their managers, doesn't appoint a new manager until the end of the season (very unusual) Can someone clear my doubt please?
Based on the data given, we're really just comparing the dismissal rates of the managers who start the season. If we also included those managers who replaced the dismissed managers, then it would be more complicated, as we'd need to consider how long they "survived" from their apppointment.
