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.
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.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please answer all parts of the question, thank you
Transcribed Image Text: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
P
5.2
1.50 -0.40 -0.30
-0.09
5.4
-0.06
5.6
-0.20 -0.10
-0.03
‒‒‒‒‒‒
11
5.8
Outcomes
-0
Differences
0
11
6
a) What type of resampling method is this?
6.2
0.03
Mean difference
narrow
Mean = 5.725
SD = 0.368
wide
Mean = 5.708
SD = 0.429
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:
0.06
11
6.4
11
0.10 0.20 0.30 0.40 0.50
N
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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