How can I convince my teacher that he is wrong in this task? We were given the following task and my teacher says I have to use a z-test. In my opinion I have to use a t-test.The task is as follows:
A company installs a nuclear power blocker into the power grid to improve the health of its employees. Before installation, employees had an average of 12.7 sick days per year over the years with a standard deviation of 1.2 days. In the two years following installation, the average was 11.4 sick days. Determine whether health has actually improved using a 95% confidence interval assuming that the standard deviation has not changed. Can it be confirmed that the health of the employees has improved?
I calculated the t test because there is a rule that if the sample n, in this case the 2 years, are smaller than 30, then it should you can use the t-test. Since n=2 and less than 30, I thought the t-test was the right choice. Can I use this rule and are there other options too, that proof that the t-test is the right choice? The formula is following: t = (X-u)/(s/root(n)) . X is the sample mean which is 11.4, s is the stnadard deviation with 1.2 . u is the normal mean with 12.7 and n is the sample which is 2. t = (11.4-12.7)/(1.2/root(2)) . This is the way I calculated it to get the to get the test value. Click for the n<30 then t-test rule