Question

In R if possible too, please:

Entanglement of marine mammals in fishing gear is considered a significant threat to the species. A study published in Marine Mammal Science (April 2010) investigated the type of net most likely to entangle a certain species of whale inhabiting the East Sea of Korea. A sample of 207 entanglements of whales in the area formed the data for the study. These entanglements were caused by one of three types of fishing gear: set nets, pots, and gill nets. One of the variables investigated was body length (in metres) of the entangled whale.

1. Set up the null and alternative hypotheses for determining whether the average body length of entangled whales differs for the three types of fishing gear.

2. An ANOVA F-test yielded the following results: ? = 34.81, ? ????? = .0001 ???? Interpret the results for ? = .05.

3. Identify the associated ? value for the results above from the ? Table and support the findings above with a diagram illustrating the rejection region.

4. Interpret the ANOVA ? MSE components.

Answer 1

1. Null hypothesis:

The mean body length of entangled whales are the same for the three types of fishing gears.

Alternate Hypothesis:

The mean body length of entangled whales differs for at least two types of fishing gears.

2. The p-value for the test is 0.0001<0.05, we reject the null hypothesis. Hence, we conclude that there are enough evidences that the  the average body length of entangled whales differs for the three types of fishing gear.

3. Here, the df for the fishing gear(Between groups) is 3-1=2. The total df =207-1=206. The error df =206-2=204. Hence the associated F-Critical value is F(2, 204) at 5% level is 3.0402.

4. The calculated value of F is 34.81 which is greater than the critical value of F making the Between groups variance significant. In other words, the MS(between groups)=34.21 times that of Mean square error for the error.