biostats question. If you can answer A. that\'s would be phenomenal, B if you ar

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biostats question.

If you can answer A. that's would be phenomenal, B if you are feeling exceptional. Thank you!

2. Mountain pine beetles (Dendroctonus ponderosae) are native to Washington forests and can have periodic outbreaks where they will kill hundreds of coniferous trees resulting in large patches of dead trees often seen in satellite images of the Cascade Mountains. A recent study was conducted to determine if the average density of Dendroctonus ponderosae is the same on different species of coniferous trees on the Okanagan-Wenatchee National Forest near Ellensburg. The dataset below shows the results of the field study Tree Species Ponderosa Pine Douglas Fir Douglas Fir Silver Fir Ponderosa Pine Douglas Fir Grand Fir Silver Fir Ponderosa Pine Silver Fir Grand Fir Ponderosa Pine Grand Fir Silver Fir Grand Fir Douglas Fir Number of larvae per m2 451 332 512 478 125 369 352 289 412 501 371 228 403 544 301 298 a) Name the appropriate statistical test that should be conducted to determine if a difference exists between tree species with respect to beetle larvae der nsity. (6 pts) b) Give a brief justification as to why the test you chose is the appropriate test. (5 pts)

Explanation / Answer

(a) We can use a t-test for independent samples to test if the average larvae density of DENDROCTONUS PONDEROSAE is the same on different species of coniferous trees (Pine and fir) in the area under study.

The basic assumption in the application of a t-test to a set of sample observations is that the underlying population(s) from which the sample(s) is (are) drawn is normally distributed. This is a very important condition for the application of a t-test.

The following assumptions are made in the application of a student’s t-test when testing for difference in two sample means:

Null hypothesis and Alternative hypothesis

The null hypothesis (H0) in a t-test involving two population means is that the two population means are equal, that is µx=µy

The alternative hypothesis (H1) gives a counter claim about the nature of the relationship between the two population means This could be µxµy ; for this type of counter assertion we use a two tailed this

Since, we want to test if the two population means differ significantly or not a t-test for difference in means for independent samples will be appropriate.

(b) This test is appropriate because it satisfies the following conditions:

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