Question

1. A scientist collects fish from two lakes. The first lake is known to have large fish and the second is known to have small fish. The fish caught from the first lake have weights, in grams, of: c(41.4, 35.9, 35.7, 29.9, 48.3, 36.7, 37.2, 29.7, 45.5) and fish caught from the second lake has weights of: c(41.9, 35.4, 35.4, 23.9, 34.4, 39.9, 34.2, 42.3) Is there evidence that the first group is actually more active than the second? （Pls show the R code）

(a) State a sensible null hypothesis

(b) State the precise definition of p-value and explain what “more extreme” means in this context (

c) Is a one-sided or two-sided test needed? justify

(d) Perform a student t-test using R and interpret

Answer 1

We first input the data in R and calculate the sample variances as shown below:

Thus, we see that the sample variances of the two samples of fish weights from the two lakes differ. So, the underlying Normal population may be assumed to have unequal variance.

We proceed to define the underlying Normal Populations and then answer part (a) , (b) and (c)

For part (d) :

We use the t.test() command in R for performing the Student t test.

The interpretation is provided at the end of the code as comment.