the appropriateness of t-test Two different Universities record data on students who are unable to attend classes due to illness. University 1 recorded absences over ten consecutive days. This data is recorded as N1 below. University 2 recorded absences over six consecutive days. This data is recorded as N2 in below. 
$N1: 9, 9, 5, 5, 5, 6, 16, 8, 8, 7$ (10 points) 
$N2: 13, 11, 14, 13, 12, 11$ (6 points)
a) Assuming equal variances, using a two sampled t-test, determine whether there is a difference between means.
I have done this one and found that: The absolute value of the test statistic in this example, 3.2066, is greater than the critical value of 2.1448, so we reject the null hypothesis and conclude that the two population means are different at the 0.05 significance level. 
b) Could you please comment on the appropriateness of the test?
c) In a related study, you observe that when students are ill, they take on average five days off. How would this affect the appropriateness of using a t-test described above.
Could anyone give me some advices/insights on solving the b, c questions?

b) The t-test (or z-test for that matter) are generally only used if the samples are coming from a population that is normally distributed, or if the samples are relatively large.  In this case, there is no indication from the question that the number of absences per day follows a normal distribution, and the sample sizes are rather small, so it may be more appropriate to use a non-parametric test (such as the Wilcoxon Rank Test).
c) If a student who is sick takes an average of 5 days off, then the number of absences from one day to the next are not independent. This further makes the t-test inappropriate, as the t-test is designed for cases where the sample items are independent from one another.
