Hypothesis Testing

Cedar-apple rust is a disease that affects apple trees and causes rust-coloured spots on the leaves. Red cedar trees are the primary source of the fungus that infects the apple trees. An experiment was conducted to determine the effect of removing all red cedar trees within 100 yards of the orchard. In year 1 the numbers of leaves with rust spots on each of 8 trees were counted. All red cedar trees within 100 yards of the orchard were felled in the winter and the following year the same trees were examined for rust spots. The results were as follows:

Tree 1 2 3 4 5 6 7 8
Year 1 38 10 84 36 50 35 73 48
Year 2 32 16 57 28 55 12 61 29

Stating clearly any assumptions that you make, carry out a suitable hypothesis test to determine whether the removal of the red cedar trees has reduced the mean number of leaves with rust spots


I have begun by finding the sample mean of the year 1 data which is 46.75.
Would by text hypothesis be:

H0: μ=46.75 versus H1:=μ<46.75?

Not quite, I think here the idea is to use a paired t-test...

http://www.statstutor.ac.uk/resources/uploaded/paired-t-test.pdf

So your H0 would be Mu1 = Mu2 (iirc..)

Youtube examples if you're stuck.

Thank you that makes more sence! Would it still be a one sided test, ie would it be

H0: Mu1=Mu2 versus H1: Mu1>Mu2 as it asks to determine whether the removal of the red cedar trees had REDUCED the mean number of leaves with rust spots?

Correct nice one

Sorry, one last question because I'm confusing myself

Would the sample size be 8 because there at 8 trees or would it be the number of leaves with rust spots ie add up all the values of year 1?

No worries ask as many as you like.

It is the trees, never the sum of observations.

Thank you, I think i have done it so i wondered if you could take a quick look.
Obviously i dont expect you to do the calculators I just wondered if you would be able to have a quick look over to check the method is correct.

My stats is a bit rusty, I remember pooled variance but I thought that was for when you use F distributions... I suppose I should check my textbooks.

http://www.statisticssolutions.com/manova-analysis-paired-sample-t-test/

But it may be worth reading that, that was the method I had in mind rather than invoking pooled variance

If my test hypothesis is
H0: u=0 versus H1: u<0 is this an upper or lower tailed test