4. In the Rundle fly lab we use both narrow and wider glass vials to house insects. A student in the lab was interested in whether these differ in mean 'lifespan' (i.e. how long they last before breaking), so she created 41 pairs of vials (one narrow and one wide) that were always used together and recorded how many months each vial survived before breaking. In the upper panel below, 'Outcomes' is the age at breaking (in months) with narrow vials shown along the top, wide along the bottom, with a line connecting each pair. The panel below shows the differences (age of breaking of narrow - age of breaking of wide) for each of the 40 pairs. 5 5.2 -0.09 5.4 1.50 -0.40 -0.30 -0.20 -0.10 -0.06 11 5.6 -0.03 ET 5.8 Outcomes -0 Differences 0 6 a) What type of resampling method is this? 6.2 For her statistical analysis, she used a resampling method in which, with a 50% probability, the ages of the two members of a given pair were swapped (i.e. flip a coin, heads means the values stay as they are and tails mean they are swapped so the narrow value becomes the wide and vice versa). This was repeated for all pairs to generate a new dataset from which she calculated the mean difference as described above. She repeated this 5000 times, the results of which yielded the following distribution of mean differences: 0.03 Mean difference narrow Mean = 5.725 SD = 0.368 ‒‒‒‒‒‒ wide Mean = 5.708 SD = 0.429 0.10 0.20 0.30 0.40 0.50 6.4 0.06 Mean = 0.017 SD = 0.171 6.6 Mean= -0.000 SD = 0.027 0.09 b) Explain the 3rd (i.e. last) figure in the question. What does it show? c) From the above, is the observed difference in mean lifespan of the wide vs. narrow vials statistically significant (assuming a = 0.05 and a two-tailed test)? Briefly explain how you arrived at your answer.

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