Question

1. There were 2 two species of rare caiman found in a river in Colombia.  Scientists want to know if species A is significantly larger than species B based on the sampling of mass from these two populations.  Help them out and conduct the proper t-test to tell them if their hypothesis is correct or not.

Population A (mass, kg)

46.25 43.52 49.93 48.04 38.37 52.96 48.13 52.00 48.69 52.93 49.68 54.71 47.16 41.68

Population B (mass, kg)

42.48 35.91 39.38 40.00 31.95 40.76 32.72 39.37 35.79 39.14 45.03 28.21 36.98 42.06

34.07 32.36

1. What is the null and alternative hypotheses?
2. Is the data normally distributed?
3. Which type of t-test and why and calculate the t-statistic (by hand, show your work)
4. Now in R – code & results
5. What can you conclude based on this analysis?

Answer 1

We are using a two independent samples t test because we have been given 2 independent populations and also because the two population standard deviations are not known to us.

(d) The R code and the results are given below:

> x1=c(46.25, 43.52, 49.93, 48.04, 38.37, 52.96, 48.13, 52.00, 48.69, 52.93, 49.68, 54.71, 47.16, 41.68)
> x2=c(42.48, 35.91, 39.38, 40.00, 31.95, 40.76, 32.72, 39.37, 35.79, 39.14, 45.03, 28.21, 36.98, 42.06, 34.07, 32.36)
> t.test(x1,x2,mu=0,,var.equal=T,paired=F)

Two Sample t-test

data: x1 and x2
t = 6.5059, df = 28, p-value = 2.372e-07
alternative hypothesis: true difference in means is greater than 0
95 percent confidence interval:
8.037591 Inf
sample estimates:
mean of x mean of y
48.14643 37.26313

(e) From the above result, we see that since the p-value is less than 0.05, we reject the null hypothesis. We conclude that there is enough evidence to suggest that species A is significantly larger than species B based on the sampling of mass from these two populations.