In a study of hearing loss, endolymphatic sac tumors (ELSTs) were discovered in 13 patients. These 13 patients had a total of 15 tumors (i.e., most patients had a single tumor, but two of the patients had 2 tumors each). Ten of the tumors were associated with the loss of functional hearing in an ear, but for 5 of the ears with tumors the patient had no hearing loss. A natural question is whether hearing loss is more likely with large tumors than with small tumors. Thus, the sizes of the tumors were measured. Suppose that the sample means and standard deviations were given and that a comparison of average tumor size (hearing loss versus no hearing loss) was being considered.
(a) Explain why a t test to compare average tumor size is not appropriate here.
(b) If the raw data were given, could a Wilcoxon-Mann-Whitney test be used?