Most frog species have distinctive calls that are used to attract mates, but several lineages of frogs have lost both the ability to call (through loss of the vocal sac) and to hear airborne sounds (through loss of the tympanum and middle ear). An evolutionary biologist hypothesizes that these losses are more common in diurnal species due to increased risk of predation when calling during the day. To test this, she determines the daily activity patterns of the 38 frog lineages that have lost vocal sacs and middle ears and finds that 16 are diurnal.

Following the scenario outlined in Q1, a second hypothesis occurs to the researcher. She hypothesizes that brightly coloured frog lineages are more likely to lose ears and vocal sacs than dull coloured lineages due to higher visibility to predators. She randomly selects 30 species that have experienced ear and vocal loss and 30 species that have not. In her original research proposal, she stated she would use a one-tailed statistical test to analyze the data. After doing so, she does not reject the null hypothesis. Her colleague points out that switching to a two-tailed test would result in rejection of the null hypothesis; a more interesting (and publishable) result.

a) What type of study is this? Briefly explain and be specific. (2 marks)

b) What pattern was most likely evident in the data, that prompted her colleague to make the suggestion? (1 mark)

c) What problems, in terms of statistical errors, could arise if she follows the suggestion? Briefly explain your answer. (2 marks)

d) What other statical problem is likely to arise from the study design? Briefly explain. (1 mark)

e) Assume that bright colouration does influence likelihood of ear and vocal loss. What type of error has been committed and what would be an appropriate way to rectify the error. Briefly explain. (2 marks)

f) What statistic(s) could be calculated from the data to determine how likely a brightly coloured frog species is to lose the ears and vocal sac compared to a dull frog species? Briefly explain your answer. (2 marks)

g) Calculate the statistic(s) you mentioned in f) based on the following: 20 bright species with ear/vocal loss and 15 dull species without. (1 mark)