Reference no: EM133482076

Question: Your supervisor has a theory that sex ratios in the eggs of certain species of crocodile depends on the temperature at which they are incubated. Her rival at a big American university is sure that egg sex ratio is determined by humidity (and believes it can make a difference of as much as 40-50% difference in the proportion of males vs females) but your supervisor is a strong opponent of this idea. 

1. On her instruction, you collect 23 eggs, and incubate 12 of them at a low humidity and 11 of them at a high humidity.  You find that 3 of the 12 are male and 8 of the 11 are male. You run the appropriate test to test whether there is a difference in male-female proportion (make sure you do it!) and your supervisor wants to know what p-value you get. You tell her. She is overjoyed and asks you to start writing a paper entitled 'Humidity does not affect crocodile egg sex ratio'. What do you say to her? 
2. Later, you conduct another experiment where you aim to incubate eggs at several different temperatures (low, medium and high... say 25^oC, 28^oC and 31^oC), to see how this affects sex ratio. Only three or four eggs fit in each incubator at a time, but luckily you have access to lots of incubators! Unfortunately, when you test the incubators with an independent probe that you know if highly accurate, you find that the thermostats in the incubators are not very accurate and thus it is impossible to get each incubator to be exactly the same temperature. For example, an incubator set to be at 28^oC may actually reach a temperate of 28.5^oC or 27.1^oC or 29.2^oC. So you put three or four eggs in each incubator, record the actual temperature reached in each incubator using the probe that you know if highly accurate, incubate the eggs for the relevant time at that constant temperature, and then for each egg you record whether it ends up male or female. You find that each incubator was actually at a different temperate, but the range of temperatures achieved in the incubators covered the range of temperatures that you are interested in. When you discuss the analysis with your supervisor, she assumes that you will calculate the proportion of males for each incubator, and then conduct a standard one-way ANOVA with three levels to test whether proportion of males varies with temperature. What do you say to her?
3. Later, you tell her that you also accurately measured the actual humidity in each incubator, and after conducting an appropriate analysis, you got the results summary below. When she sees the summary, she is again overjoyed and asks you to start writing a paper entitled 'Temperature affects crocodile egg sex ratio, but humidity does not'. What do you say to her?