Question

You are working on a conservation farm with an endangered species of antelope in central Colorado. You notice that birth weight of offspring seems to correlate with air temperature, but that the relationship is not as strong in females as in males. You wonder why that could be.

a) What is your testable hypothesis?

b) Design an experiment to test that hypothesis.

c) What is your null hypothesis?

d) Describe the type of data you will get from the experiment.

e) What type of statistical analysis will you do, and why is it appropriate?

f) Make up some data – at least 10 total. Run your test and show your calculations.

g) What do your results tell you about your hypothesis?

Answer 1

Answer: ---- Date: ---10/4/2020 a) A testable hypothesis can be "Birth weight of male antelopes are higher than female antelopes when exposed to the same temperature at birth" b) The experiment can go as follows: 1. All the antelopes should be exposed to the same air temperature for a certain period since the beginning of their pregnancy 2. Since the birth weight of males and females are being studied with respect to air temperature, all other parameters on which birth weight depends should be kept constant 3. Two batch of antelopes, one of each batch being seperately exposed to a higher temperature and a lower temperature, so that a comparison study can be done to see the effectiveness of the relationship of birth weight with air temperature 4. Individual antelopes can be also exposed to various varying temperature to see the effect on the birth weight on a gender wise basis This experiment can help classify the antelopes to obtain data on basis of the factors for doing the appropriate analysis c) (0) A possible null hypothesis for this problem can be given as: HO: PF =0 (there is no relationship between air temperature and female off-spring birth weight) H1: HO is not true

Generally, we need to test whether air temperature and birth weight are correlated, so we take the null hypothesis as "not correlated" (ii) Another possible null hypothesis can be : HO: MM-MF ( Mean birth wt of males Mean birth weight of females) d) The data from the experiment are the weights of the offspring at birth, air temperature at birth and gender of the offspring e) A correlation test for the hypothesis in c(i) can be used since it is used to test the hypothesis whether the air temperature and the body weight at birth for female offsprings are correlated or not. Similar tests can be done for male offsprings too. If things go well, a regression model can also be used to predict the outcomes and validate the assumprtions f) The analysis is done using a simulated data in R as below [for the hypothesis c0): Under HO, the correlation test test-statistics follows a t-distribution with df n-2, n=number of observations. So, here in this example, we have taken n=10. Here we are basically proving that increasing air temperature doesn't have effect on the body weight of the offsprings born as females

Source on Save 7. Run + Source - wt<-c(3.1.2.1.8.1.97.4.5.23,5.8.2.4.1.7.3.2) temperature<-c(11:20) corr_sampc-cor (temperature, wt) n<-length(wt) test statistic-corr_samp sqrt(n-2)/sqrt(1-corr_samp 2) #P(t8>test statistic) test statistic p_value 2(1-pt (test_statistic.8)) #As it is a 2-sided test, HO: corr0 vs HO: corr!.0, where "!" stands for "not equal to" 6 9.1 Top Level: Console Terminal >w<-c(3.1.2.1.8.1.97.4.5.23,5.8.2.4,1.7.3.2) > temperature<-c(11:20) > length(wt) [1] 10 > length(temperature) (1) 10 > corr sampe-cor (temp.wt) Error in cor (temp. wt) : incompatible dimensions > corr_sampc-cor(temperature, wt) > corr samp [1] 0.1820837 > #P(t8>test_statistic) > test statistic Error: object 'test_statistic' not found >n<-length(wt) > test_statistica-corr-sampesqrt(n-2)/sqrt(1-corr_samp^2) >#PCt8>test statistic) > test statistic (1) 0.5237662 > p_value=2pt(test_statistic, 8) > P value (1) 1.385363 > p_value=2*(1-pt(test_statistic, 8)) > p_value (1) 0.614637

g) The p_value (p-value) is greater than 0.05, 0.01 so at both 5% and 1% level of significance, we accept the null hypothesis, and conclude that there is no correlation, i.e,, no relationship between the birth weight of females and air temperature at birth for the female born off-spring (for this example point of view). Although this is just a simulated dataset, the analysis can proceed in a similar way of such data points are available for the male off springs too. A skeleton of the data frame that can be collected from the experiment is given as below: 1 2 3 Source on Save airtemp<-rnorm(10,15,1) wt<-rnorm(10,6,2) gender<-c("F","M","M","M","F","M","F", "F","F","M") data-data.frame(airtemp.wt, gender) 5:1 (Top Level) : Console Terminal > airtemp<-rnorm(10,15,1) > wtc-rnorm (10.6.2) > gender<-c("F","M","M","M","F","M","F","F" "F" "M") > data<-data.frame(airtemp.wt.gender) >data airtemp wt gender 1 14.48571 5.281235 2 15.86779 5.882339 3 16.02646 6.724062 4 15.68622 7.890936 5 14.55756 8.936293 6 15.72067 5.690569 7 13.48513 5.437068 8 12.77236 7.540657 9 16.19781 5.991993 10 13.65098 10.387051